Upload
teresa-pulga
View
230
Download
0
Embed Size (px)
Citation preview
7/26/2019 Compilation in Physics 212
1/113
7/26/2019 Compilation in Physics 212
2/113
surface repeatedly. 'or sound waves the disturbance is a change in air
pressure perhaps created by the oscillating cone inside a speaker. 'or
earthquakes there are several types of disturbances including disturbance of
Earths surface and pressure disturbances under the surface.
% wave is a disturbance that propagates or moves from the place it was
created. The simplest waves repeat themselves for several cycles and are
associated with simple harmonic motion.
The wave is an up and down disturbance of the water surface. It causes a
sea gull to move up and down in simple harmonic motion as the wave crests
and troughs (peaks and valleys) pass under the bird. The time for one complete
up and down motion is the waves period T. The waves frequency is f * + T as
usual. The wave itself moves to the right in the $gure. This movement of the
wave is actually the disturbance moving to the right not the water itself (or the
bird would move to the right). #e de$ne wave velocity vw to be the speed at
which the disturbance moves. #ave velocity is sometimes also called the
propagation velocity or propagation speed because the disturbance propagates
from one location to another.
Figure 16.30%n ideali,ed ocean wave passes under a sea gull that bobs up and down in
simple harmonic motion. The wave has a wavelength which is the distance between ad-acent
7/26/2019 Compilation in Physics 212
3/113
7/26/2019 Compilation in Physics 212
4/113
Figure 16.31 In this example of a transverse wave the wave propagates hori,ontally and
the disturbance in the cord is in the vertical direction.
Figure 16.3% In this example of a longitudinal wave the wave propagates hori,ontally and
the disturbance in the cord is also in the hori,ontal direction.
#aves may be transverse longitudinal or a combination of the two. (#ater
waves are actually a combination of transverse and longitudinal. The
simpli$ed water wave illustrated in Figure 16.30 shows no longitudinal
motion of the bird.) The waves on the strings of musical instruments are
transverse2so are electromagnetic waves such as visible light.
0ound waves in air and water are longitudinal. Their disturbances are periodic
variations in pressure that are transmitted in 3uids. 'luids do not have
appreciable shear strength and thus the sound waves in them must be
longitudinal or compressional. 0ound in solids can be both longitudinal and
transverse.
In both cases (and in all other forms of wave motion) the disturbance moves
through the medium (slinky string water air whatever....) with only a minimal
motion of the medium itself. #hat is being described in the equations of wave
motion is the motion of the disturbance. The wave speed for example is the
speed at which the disturbance moves.
4y(x 44
7/26/2019 Compilation in Physics 212
5/113
t)
v
y(xt)
t4 x 4
%s seen in the derivation for a wave on a string it is -ust 5ewton6s second law
applied to a small part of the string itself. The most general solution to this
equation is any function of the argument (x7vt) and v is the speed at which the
wave propogates. That is any function of x and t that has the form
The most general form of the di"erential equation that describes a mechanical
wave is written8
y(xt)f (x 7vt)
would solve the above di"erential wave equation with v being the speed of the
disturbance (ie the wave) through the medium. The speci$c form of the wave
would depend on the source of the disturbance (a hand clap would be di"erent
than a tuning fork) ! but the wave speed itself would depend on the medium
through which the disturbance travelled. The direction of propagation is
determined by the sign in the argument. f(x9vt) corresponds to a wave
traveling to the left a :!: sign is to the right.
Wave &r!'aga"i!n S'ee
The wave speed is determined by properties of the medium (except for light
which travels at speed of ;x*
7/26/2019 Compilation in Physics 212
6/113
'or a transverse wave on a taut string or a longitudinal wave on a stretched
:slinky: the wave speed is dependent on the linear mass density of the string
(ie the mass per unit length ?) and the tension in the string or the slinky ('). Ie
v= F
'or sound waves through air or water the wave speed would depend on the
compressibility of the medium and the volume mass density (since a
disturbance can propagate in all directions in a three dimensional medium).
0ince water is nearly like a solid with respect to compressions it should not be
surprising that sound travels faster through water than through air (even
though the mass density is a thousand times as great).
&any important examples of wave motion involve a wave function that is
sinusoidal. That is rather than a single pulse that propagates the disturbance is
in the shape of a sine wave. The resulting wave motion description is then
y(xt)Asin(kx 7t)
It is not di@cult to show that this equation in fact is a solution to thedi"erential wave equation by -ust taking derivatives of y(xt) and substituting
into the di"erential equation. #hen that is done one can see the connection
between the wave speed and the constants k and . The wave number as k is
called is -ust 4A divided by the wavelength. The angular frequency has the
same meaning in wave motion as it does in simple harmonic motion or circular
motion. %nd the wave speed wavelength and frequency are always related in
the same way.
k
4
and 4f
4
and v f T
These relationships are always true.
7/26/2019 Compilation in Physics 212
7/113
5otice that for any speci$c time t the shape of the wave as you move along
the string (ie y vs x) is -ust that of a sine function. %nd if you consider only that
part of the wave at a speci$c location x the motion of the medium itself is
simple harmonic with an amplitude % and angular frequency.
Biven the relationships between k f T and the wave function y(xt) can
be written in a variety of ways. They are all equivalent.
y (x , t)=Asin (kx 2ft)=Asink(x vt)
The amplitude of the wave is -ust the maximum displacement of any part of
the medium from the equilibrium or undisturbed position. The frequency and
period of the oscillation the wavelength the wave number etc. and the wave
speed are then related by the equations above. 'or a wave on a string the
wave speed is still dependent on the mass density and the tension by v=F . Su'er'!si"i!n an In"er(eren)e
In general the idea of superposition of waves is common to all types of wavemotion. The standing wave problem discussed in the waves!on!a!string
discussion is simply the result of two identical waves traveling in opposite
directions as shown previously. The superposition of two waves traveling in the
same direction will lead to the ideas of constructive and destructive interference
and will be important in both sound and light. >ut the mathematics is most
easily developed using the equations of harmonic waves to describe waves on a
string.
0uppose two identical waves are traveling in the same direction and they
di"er only in that there is a phase di"erence between them. That is the waves
y*(xt) and y4(xt) are the two waves described by
y*(kx t) and y4(kx t 9)
7/26/2019 Compilation in Physics 212
8/113
The wave descriptions can be rewritten by adding and subtracting +4 in each
argument. 'or the sake of the derivation we can then let kx!wt9+4. The
total combined wave is then written8
y*(kx t 9+ 4+ 4)9y4(kx t 99+ 4+ 4)y*(+ 4)9
y4(9+ 4)
Csing trigonometric identities to break sin(7+4) into products of sines and
cosines yields the following result8
ytotal(xt)4Acos(+4)sin(kx t 9+ 4)
This equation represents the combined wave equation. 5otice that it simply
represents a traveling wave with the same frequency and wavelength as the
constituent waves but with an amplitude 4%cos(+4) that depends on the phase
di"erence . #hen .
7/26/2019 Compilation in Physics 212
9/113
7/26/2019 Compilation in Physics 212
10/113
7/26/2019 Compilation in Physics 212
11/113
Cri"i)a# Da+'ing the condition in which the damping of an oscillator
causes it to return as quickly as possible to its equilibrium position
withoutoscillating back and forth about this position
De(!r+a"i!n displacement from equilibrium
Des"ru)"ive In"er(eren)e when two identical waves arrive at the same
point exactly out of phase1 that is precisely aligned crest to trough
E#as"i) &!"en"ia# Energ* potential energy stored as a result of
deformation of an elastic ob-ect such as the stretching of a spring
F!r)e C!ns"an" a constant related to the rigidity of a system8 the
larger the force constant the more rigid the system1 the force
constant isrepresented by k
Freuen)* number of events per unit of time
Funa+en"a# Freuen)* the lowest frequency of a periodic waveform
In"ensi"* power per unit area
L!ngi"uina# Wave a wave in which the disturbance is parallel to the
direction of propagation
7/26/2019 Compilation in Physics 212
12/113
Na"ura# Freuen)* the frequency at which a system would oscillate if
there were no driving and no damping forces
N!es the points where the string does not move1 more generally nodes
are where the wave disturbance is ,ero in a standing wave
Os)i##a"e moving back and forth regularly between two points
Over Da+'ing the condition in which damping of an oscillator causes
it to return to equilibrium without oscillating1 oscillator moves more
slowlytoward equilibrium than in the critically damped system
Over"!nes multiples of the fundamental frequency of a sound &eri!i) M!"i!n motion that repeats itself at regular time intervals
&eri! time it takes to complete one oscillation
Res!nan)e the phenomenon of driving a system with a frequency equal
to the system6s natural frequency
Res!na"e a system being driven at its natural frequency
Res"!ring F!r)e force acting in opposition to the force caused by a
deformation Si+'#e ar+!ni) M!"i!n the oscillatory motion in a system where the
net force can be described by Gookes law
7/26/2019 Compilation in Physics 212
13/113
Si+'#e ar+!ni) Os)i##a"!r a device that implements Gookes law
such as a mass that is attached to a spring with the other end of the
springbeing connected to a rigid support such as a wall
Si+'#e &enu#u+ an ob-ect with a small mass suspended from a light
wire or string
Su'er'!si"i!n the phenomenon that occurs when two or more waves
arrive at the same point
Transverse Wave a wave in which the disturbance is perpendicular to
the direction of propagation Uner Da+'ing the condition in which damping of an oscillator causes
it to return to equilibrium with the amplitude gradually decreasing to ,ero1
system returns to equilibrium faster but overshoots and crosses the
equilibrium position one or more times
Wave Ve#!)i"* the speed at which the disturbance moves. %lso called
the propagation velocity or propagation speed
Wave#eng"2 the distance between ad-acent identical parts of a wave
Wave a disturbance that moves from its source and carries energy
7/26/2019 Compilation in Physics 212
14/113
7/26/2019 Compilation in Physics 212
15/113
7/26/2019 Compilation in Physics 212
16/113
cm. If the cork is 4 m from the edge of the pool how long does it take a
ripple passing the cork to reach the edgeN
Solution:
Biven8 wavelength of 4< cmcork is 4 m from the edge of the pool
Mequired8 time required to take a ripple passing the cork to reach the
edge
'ormula8The time taken for the ripple to reach the edge of the pool is obtained
from8
t=D
v v=D
t
#e know thatv=f
Therefore
t= D
f
t= 2m
1Hz 0.2m
t= 2m1 s
1 0.2m
t=10 s
. alculate the fundamental frequency for a string
7/26/2019 Compilation in Physics 212
17/113
f 0+4JKT+mL *+
4DO by using the approximate correction of
7/26/2019 Compilation in Physics 212
18/113
'ormula8
=. % sound wave traveling at ;< m+s has a frequency of
7/26/2019 Compilation in Physics 212
19/113
4< vibrations
Mequired8 wavelength of sound
'ormula8
#avelength DistanceNo . of osciations
25
20
*.4 ms!*.
*
7/26/2019 Compilation in Physics 212
20/113
7/26/2019 Compilation in Physics 212
21/113
Biven8 frequency of *< G,wavelength
7/26/2019 Compilation in Physics 212
22/113
Chapter 2+ )o$n!
DISCUSSION AND DERIVATION OF
FORMULAS IN SOUND
SOUND
This study of sound will concentrate on only a few main ideas ! sound as
an example of a longitudinal wave exhibits all the properties that all waves
exhibit including a speed that depends on the medium that carries the wave
and both interference and di"raction. 0ound level measurements (the
decibel scale) are related to the energy density in the wave and the
apparent frequency of the sound one hears depends on both the speed of
the source and the speed of the listener relative to the speed of sound in air
(the Foppler e"ect). The most general study of sound would include
discussions of how sound propagates through air as well as in liquids and
7/26/2019 Compilation in Physics 212
23/113
solids our perceptions of sound ! which would require understanding the
physiology of hearing and would ultimately lead to the study of musical
instruments and the complex study of acoustics.
S!un as a $aveThe general principles studied in the discussion of wave motion apply
equally well to sound. That includes of course the most general
relationships between wave speed wavelength and frequency8 That is
v f
where represents the wavelength and f is the frequency. The wave speed v
is determined by properties of the medium ! which we will consider is air. The
wave itself is longitudinal rather than transverse as are waves on strings and
the surface waves on water. >ut the waves propagate in all directions as a
speed determined by the compressibility and mass density of the air. The
propagation of a disturbance in air is described by a di"erential equation of
the same form as for transverse waves on a taut string. 0o the solutions to
the equation are necessarily of the same form as well. That is a disturbance
in air is governed by a wave equation of the form
!2y (x , t)
! t2 =v2
!2y (x ,t)
! x2
which has solutions representing waves traveling a speed v that depends on
the bulk modulus > (whichin turn depends on pressure and temperature) and
on the mass density of the air. That is the disturbance that propagates
through the air that we call :sound: can be described with the same type ofwave equation that was used to describe waves on strings. %nd the speed of
those waves depends on properties of the medium through which they
travel.
7/26/2019 Compilation in Physics 212
24/113
v="#where plays the same role as the tension in the string and is the mass
per unit volume of the air rather than the linear mass density of the string
which supported a transverse wave.
In air the wave speed can be related to the air temperature by
v
-
T (;;*
m+s)
T
4/
;M
where is a constant for air M is the Cniversal Bas onstant & is the
average molecular mass of air and the temperature is the %bsolute
temperature on the Pelvin scale. The equation can be simpli$ed in terms of
the speed of sound in air at 4/; P (ie ice point).
S!un In"ensi"*
The intensity of a wave is simply the energy per unit time that is
transferred per unit area of a surface that the wave impinges on. >ut energy
per time is -ust the power that is delivered by the source. %nd that energy is
distributed over an ever increasing area as the wave propagates away from
the source. %ssuming a point source of sound with waves spreading outward
in spherical wave fronts ! and assuming no energy dissipation as the wave
propagates through the air ! the intensity decreases as the inverse square of
the distance from the source as the energy is spread over an ever increasing
spherical surface. 0o the intensity or power per unit area is simply given by
7/26/2019 Compilation in Physics 212
25/113
Intensity in watts+m4 I Qavg+D r4
where Qavgis the power emitted by the source and r is the distance from the
source. The intensity I would be measured in watts per square meter In
practice the intensity of a sound is much more complicated since the above
expression assumes a point source of sound that spreads out 0ound source
uniformly in all directions. Ignored in this expression is the absorption of
sound by the air itself and re3ections from surfaces that the sound
encounters.
Braphing the intensity as a function of distance from the source shows
how intensity diminishes as the energy of the sound waves is spread over an
ever increasing area. %s the distance from the sound source increases the
intensity decreases until it would be undetectable. The weakest sound
intensity that most humans can hear is about *
called the threshold of hearing and is assigned the symbol Io. %ll other sound
intensities can be related to Io. That is a sound intensity one hundred times
the threshold of hearing would be written I*
7/26/2019 Compilation in Physics 212
26/113
7/26/2019 Compilation in Physics 212
27/113
ideas. #e will consider interference between two identical sound waves that
are constrained to travel in a straight line but in opposite directions. This is
identical in principle to the standing waves on a string problem. 0econdly we
will consider two identical sound waves that arrive at the same point from
two di"erent sources which are separated from each other (as the sound
from two loudspeakers driven by the same signal). In general those sources
can either be exactly in phase ! or there could be a phase di"erence between
the signals produced at the speakers. This problem is identical to the
superposition and interference of two waves on a string traveling in the same
direction. The resulting wave depended on the phase di"erence between the
two signals. 'inally when two sources have slightly di"erent frequencies
there is no $xed phase di"erence between them and the super!position of
the two signals results in a varying intensity wave with a :beat frequency:
that depends on the di"erence in the individual frequencies that are being
added.
The general principle of course is the superposition principle ! that is
waves can be added to form a new wave which depends on the properties
and characteristics of the original waves. This idea treated earlier applies
equally well to longitudinal waves. %dding two waves y*(k*x7 *t) and
y4(k4x74t9) results in a wave equation that represents one of three
possibilities8 % standing wave if y* andy4 have the same frequency (and
hence wavelengths) and are traveling in opposite directions1 either
constructive or destructive interference at a particular location depending
on the phase angle at that location1 and a wave whose amplitude varies if
the two frequencies are di"erent. #e will consider each of those cases.
S"aning Wave Res!nan)es in Air C!#u+ns
The standing sound wave problem requires a one!dimensional sound
wave ! as in a sound wave created inside a hollow tube or pipe. onsider a
sound wave traveling in a tube which encounters an identical wave in the
7/26/2019 Compilation in Physics 212
28/113
opposite direction. This is identical to the situation when a wave on a string
:sees: its re3ection from the end of the string ! which leads to standing
waves. The di"erence here is that when a string is $xed at both ends there
must be a node at each end of the string. >ut a tube can have either a node
or an antinode at the ends depending on whether it is closed or open at that
end.
0ince sound is a longitudinal wave air must be able to move along the
axis of the tube. This results in the special condition that an open end of a
tube must be at an antinode of any standing wave whereas a closed end
must be a node (since air cannot move in!and!out of a closed ended tube).0o
the relationship between the length of a tube and the wavelength of the
sound when a standing wave occurs depends on whether the tube has open
or closed ends. 0tanding waves can be supported in a tube (or air column)
only if the tube lengths are the wavelengths of the sound in the tube are
related in certain speci$c ways.
O'en9O'en :!r C#!se9C#!se; Tu,e
If a tube is open at both ends antinodes must appear at the ends of the
tube for a standing wave to occur ! and that means the tube length must be
a multiple of half!wavelengths (ie the distance between antinodes will
always be +4 or or ;+4 etc). Sf course if the tube is closed at both ends
nodes appear at the ends and the condition is the same (and identical to the
standing wave resonances on a taut string). >ut with a tube closed at both
ends it is not obvious how the wave would be generated nor whether the
resonance could be heard outside the tubeR The condition for resonance and
the frequencies at which standing waves can be supported in a tube of
length J are given by
7/26/2019 Compilation in Physics 212
29/113
L=n
2 and fn=
v
=( v2L )n
where v is the speed of sound in air (ie in the air column contained within
the tube). %gain this is the same condition as for standing waves on a string
! and the frequencies are -ust multiples of the fundamental frequency given
by (v+4J) for the tube open at both ends.
If the tube has one open and one closed end there must be a node at
the closed end and an antinode at the open end for resonance to occur.
0ince the distance between a node and an antinode is +D ;+D +D etc. the
resonance condition is di"erent than for the open!open tube. In this case the
length of the tube is necessarily an odd multiple of quarter wavelengths or
L=m
4=(2n+1)
4
where m is an odd integer represented by (4n9*) for any integer n. 0o the
frequencies at which resonance can occur are
fn= v=( v4L )
m=(2n+1) f1
where f* is the fundamental frequency given by (v+DJ) for the tube closed at
one end.
DO&&LER EFFECT
#hen a car or train passes you the frequency of the sound that you hear
varies from a higher pitch as it approaches to a lower pitch as it recedes fromyou. (Fo not confuse this e"ect with the change in intensity or sound level as
it approaches and then recedes.) This Foppler e"ect is a common occurance
in everyday life when a source of sound is moving with respect to an
observer. There are really two di"erent causes for the e"ect. #hen the
7/26/2019 Compilation in Physics 212
30/113
source of the sound is moving the sound waves are compressed in front of
the source and expanded behind. >ut the sound still travels with respect to
the air at the speed of sound. 0o an observer in front of the source hears a
higher frequency than the source is emitting since the wave fronts arrive
closer together than if the source were not moving whereas an observer
behind the moving source hears a lower frequency.
If the source is stationary but the observer is moving a similar e"ect
occurs for a di"erent reason. The wavefronts spread out from the source
uniformly. >ut if the observer is moving toward the source he or she
encounters wavefronts more often ! hence hears a higher frequency. If the
observer is moving away from the source the wavefronts arrive less often !hence a lower frequency.
%ll of this can be summari,ed mathematically. The frequency one hears (f)
is always the speed at which the wave is traveling with respect to the
observer (vrel) divided by the wavelength () that is encountered by the
observer. That is
f.vrel
#.
The relative pee! vrelis -ust the di"erence betweeen the speed of
sound relative to the air and the speed of the observer ($ob) relative to
the air or
vrel.vo/$ob
where vois the speed of sound and $obis the speed of the observer. #hetherthe 9 or ! sign is used depends on the direction of the observer6s motion
relative to the source ! to be discussed shortly.
7/26/2019 Compilation in Physics 212
31/113
The wavelength that the observer encounters is the wavelength in front or
behind the source depending on whether the source is moving toward or
away from the observer. Gence
(vo/$o$rce)#fo
where fois the frequency the source produces and $o$rceis the speed of the
source. ombining these results yields. 5otice that in this form all cases are
included. That is if the source is moving the denominator is modi$ed by the
speed of the source. If the observer is moving the numerator is modi$ed.
%nd of course if both are moving then both are a"ected. The choice of
whether to use the 9 or ! sign in each case can be made by deciding
whether the speed of the source or of the observer has the e"ect of
increasing or decreasing the frequency that would be heard depending on
whether the motion of either tends to decrease or increase the separation
between the source and observer. If the gap between them is closing the
sound is Foppler shifted to a higher frequency whereas if the gap is
increasing the sound is Foppler shifted to a lower frequency ! regardless of
which is moving. The choice of sign is then made to yield that result.
7/26/2019 Compilation in Physics 212
32/113
DEFINITION OF TERMS
(Sound)
A)!us"i) I+'ean)e property of medium that makes the
propagation of sound waves more di@cult an"in!e point of
maximum displacement
/!$ Wa
7/26/2019 Compilation in Physics 212
33/113
In"ensi"* Re>e)"i!n C!e?)ien" a measure of the ratio of the
intensity of the wave re3ected o" a boundary between two media
relative to theintensity of the incident wave
In"ensi"* the power per unit area carried by a wave#!uness the
perception of sound intensity
N!e point of ,ero displacement
N!"e basic unit of music with speci$c names combined to generatetunes
Over"!nes all resonant frequencies higher than the fundamental
&2!n the numerical unit of loudness
&i")2 the perception of the frequency of a sound
S!ni) /!!+ a constructive interference of sound created by an
ob-ect moving faster than sound
S!un In"ensi"* Leve# a unit less quantity telling you the level of
the sound relative to a $xed standard
7/26/2019 Compilation in Physics 212
34/113
S!un &ressure Leve# the ratio of the pressure amplitude to a
reference pressure
S!un a disturbance of matter that is transmitted from its source
outward
Ti+,re number and relative intensity of multiple sound frequencies
T!ne number and relative intensity of multiple sound frequencies
U#"ras!un sounds above 4
7/26/2019 Compilation in Physics 212
35/113
SOLVED &RO/LEMS
(Sound)
*. %n echo was heard ;.D seconds after the sound was produced.
Temperature of the air is 4U . Gow far was the re3ectorN
Solution:
Biven8 Time8 ;.D seconds
Temperature8 %5@ C
Mequired8 Fistance
'ormula8
elocity8 ;;* 9
7/26/2019 Compilation in Physics 212
36/113
4. The $rst overtime of an open pipe produces D beats per second with a
tuning fork of D
7/26/2019 Compilation in Physics 212
37/113
Biven8 Jength8 ; cm 3.6 +
#eight8
Mequired8 Tension
'ormula8
;4 x /.4
4;D< m+s
v=Tm
2340= T
4.2x105
T=9.44 k' (Answer)
D. %n open pipe is < cm long and a closed pipe is 4= cm long. They are
sounded together to produced their fundamentals. Gow many beats
are heard per second if of sound in air is ;DD meter per secN
Solution:
Biven8
Spen Qipe8
Jength8 < cm 6 +
7/26/2019 Compilation in Physics 212
38/113
losed Qipe8
Jength8 4= cm %.B +
elocity8 3 +8s
Mequired8 >eats
'ormula8
Spen Qipe8
J8 m
8 *4 m
f*
;DD f (*4)
f* 4=. G,
losed Qipe8
J8 4.= m
8 . m
f4
;DD f (.)f4 H.D G,
>eats f4 ! f* H.D V 4=. ;
7/26/2019 Compilation in Physics 212
39/113
0(elocity of the air)8 33 +8s
Mequired8 v s (elocity of the source)
'ormula8
n2=n
1
v
vvs
350=(320Hz) 343m/ s343m /sv
v=29.4m /s (Answer)
. %n iron wire is stretched between two supports *4< cm apart. It has a
density of /. gm+cmW and a modulus of elasticity of * x *
7/26/2019 Compilation in Physics 212
40/113
v=461880.2154
4J (4)(*.4) %. +
v=f
461880.2154=f2.4
f=1.92x 103 sec(Answer)
/. %n open organ pipe whose length is H< cm is blown at a temperature of
4U . #hat is the frequency of the second overtoneN
Solution:
Biven8 Jength8 40 )+ 0.4 +
Temperature8 %5 C
Mequired8 0econd overtone (;f)
'ormula8
elocity8 ;;* 9
7/26/2019 Compilation in Physics 212
41/113
f=192.22m
3 f=576.66/sec (Answer )
=. % wood cutter makes * strokes per minute. If the sound of each stroke
reaches the observer as the axe makes the next stroke and air
temperature is 4
7/26/2019 Compilation in Physics 212
42/113
Biven8 0ound power Q %rea % m
Mequired8 Fistance
'ormula8 0ound intensity is given by
$=*
A
$=0.5+104
5m
1x 105/m2
*
7/26/2019 Compilation in Physics 212
43/113
t=1
2(3.4 )
t=1.7 sec
**. % train moving at 4 m+s is traveling towards &s. &iller who is
standing in the middle of the tracks. #hat frequency does &s. &iller
hear if the train has a horn frequency of *
7/26/2019 Compilation in Physics 212
44/113
*4. % burglar alarm is wailing with a frequency of *4
7/26/2019 Compilation in Physics 212
45/113
vs .< m+s
Mequired8 n4
'ormula8
n2=n1(v vo
v ) n2=700Hz( 340m /s+5.0m /s340m/ s ) 710.%4 Hz (Answer)
*D. Zou are in a car traveling at mph (4D. m+s). % second car is
moving toward you at the same speed. Its horn is sounding at D/ G,.
#hat frequency do you hearN
Solution:
Biven8
n* =
7/26/2019 Compilation in Physics 212
46/113
*. Zou are in a car traveling at 4< m+s. %n ambulance is behind you
traveling ; m+s in the same direction. #hat frequency do you hear if
the siren has a frequency of < G,N elocity of sound in air is ;D; m+s.
Biven8
n* < G,
v ;D; m+s
vs ; m+svo 4< m+s
Mequired8 n;
'ormula8
n3=n
1(v vo
vvs ) n3=550Hz( 343m / s+20m/s343m /s35m / s )
n3 6B.%1 Hz(Answer)
*. #hat will be the frequency if the ambulance takes overN
Solution:
Biven8
n* < G,
v ;D; m+s
vs ; m+svo 4< m+s
Mequired8 n;'ormula8
7/26/2019 Compilation in Physics 212
47/113
n3=n
1(v vovvs )n3=550Hz( 343m /s20m/ s343m / s+35m/s)
n3 469.97 Hz(Answer)
*/. 'or a pipe of length J
7/26/2019 Compilation in Physics 212
48/113
Chapter 12 y!rotatic
DISCUSSION AND DERIVATION OF
FORMULAS IN FLUIDS
F#ui
&atter most commonly exists as a solid liquid or gas1 these states are
known as the three common phae of matter. 0olids have a de$nite
shape and a speci$c volume liquids have a de$nite volume but their
shape changes depending on the container in which they are held and
gases have neither a de$nite shape nor a speci$c volume as their
molecules move to $ll the container in which they are held. (0ee Figure
11.%.) Jiquids and gases are considered to be 3uids because they yield to
shearing forces whereas solids resist them. 5ote that the extent to which
3uids yield to shearing forces (and hence 3ow easily and quickly) depends
on a quantity called the viscosity which is discussed in detail in Vis)!si"*
an La+inarF#!$ &!iseui##es La$.#e can understand the phases of
matter and what constitutes a 3uid by considering the forces between
atoms that make upmatter in the three phases.
7/26/2019 Compilation in Physics 212
49/113
Figure 11.% (a) %toms in a solid always have the same neighbors held near
home by forces represented here by springs. These atoms are essentially in
contact with oneanother. % rock is an example of a solid. This rock retains its
shape because of the forces holding its atoms together. (b) %toms in a liquid are
also in close contact but can slide over one another. 'orces between them
strongly resist attempts to push them closer together and also hold them in
close contact. #ater is an example of a liquid. #ater can 3ow but it also
remains in an open container because of the forces between its atoms. (c)
%toms in a gas are separated by distances that are considerably larger than the
si,e of the atoms themselves and they move about freely. % gas must be held in
a closed container to prevent it from moving out freely.
%toms in oli!are in close contact with forces between them that
allow the atoms to vibrate but not to change positions with neighboring
atoms. (These forces can be thought of as springs that can be stretched
or compressed but not easily broken.) Thus a solid reit all types of
stress. % solid cannot be easily deformed because the atoms that make
up the solid are not able to move about freely. 0olids also resist
compression because their atoms form part of a lattice structure in which
the atoms are a relatively $xed distance apart. Cnder compression the
atoms would be forced into one another. &ost of the examples we have
studied so far have involved solid ob-ects which deform very little when
stressed.
GDROSTATIC &RESSURE
Gydrostatic Qressure ! due to a column of 3uid of height hand mass
density # is
% . # &h
DENSITG
7/26/2019 Compilation in Physics 212
50/113
Fensity is mass per unit volume.
m
.
where8
is the symbol for density1
m is the mass1 and
0 is the volume occupied by the substance.
The 0I Cnit of density is the ecause the relative density of water is * the density of any substance
in kg m!;is its relative density multiplied by *
7/26/2019 Compilation in Physics 212
51/113
MANOMETER
Figure 11.16 %n open!tube manometer has one side open to the atmosphere. (a) 'luid depth must be the same on both
sides or the pressure each side exerts at the bottom will be unequal and there will be 3ow from the deeper side. (b) %
positive gauge pressure %g h& transmitted to one side of the manometer can support a column of 3uid of height h . (c)
0imilarly atmospheric pressure is greater than a negative gauge pressure %g by an amount h& . The -ars rigidity
prevents atmospheric pressure from being transmitted to the peanuts.
onsider the C!shaped tube shown in Figure 11.16 for example. This
simple tube is called a manometer. &ercury manometers are often used
to measure arterial blood pressure. %n in3atable cu" is placed on the
upper arm as shown in 'igure **.*/. >y squee,ing the bulb the person
making the measurement exerts pressure which is transmitted
undiminished to both the main artery in the arm and the manometer.
#hen this applied pressure exceeds blood pressure blood 3ow below the
cu" is cut o". The person making the measurement then slowly lowers
the applied pressure and listens for blood 3ow to resume. >lood pressure
pulsates because of the pumping action of the heart reaching a
maximum called systolic pressure and a minimum called diastolic
pressure with each heartbeat. 0ystolic pressure is measured by noting
the value of h when blood 3ow $rst begins as cu" pressure is lowered.Fiastolic pressure is measured by noting h when blood 3ows without
interruption. The typical blood pressure of a young adult raises the
mercury to a height of *4< mm at systolic and =< mm at diastolic. This is
commonly quoted as *4< over =
7/26/2019 Compilation in Physics 212
52/113
the elasticity of the arteries in maintaining the pressure between beats.
The density of the mercury 3uid in the manometer is *;. times greater
than water so the height of the 3uid will be *+*;. of that in a water
manometer. This reduced height can make measurements di@cult so
mercury manometers are used to measure larger pressures such as blood
pressure. The density of mercury is such that *.< mm Gg *;; Qa.
/OGLES LAW
>oyles Jaw states that when the temperature is kept constant the
volume of a given mass of an ideal gas varies inversely as the pressure to
which it is sub-ected1 therefore the product Qressure x olume of a given
mass of gas remains constant. Thus for a given mass of an ideal gas
ARCIMEDES &RINCI&LE
*.=constant(at constant temperat2re )
% body wholly or partly immersed in a 3uid is buoyed up by a force equal
to the weight of the 3uid it displaces. The buoyant force can be
considered to act vertically upward through the center of gravity of the
displaced 3uid.
F"=/2oyant force=wei'3t of )ispace) f2i)
The buoyant force on an ob-ect of volume 0that is totally immersed in
a 3uid of density#f is
#f 0& and the weight of the ob-ect is#o
g where #o is the density of the ob-ect. Therefore the net upward
force on the submerged ob-ect is
7/26/2019 Compilation in Physics 212
53/113
3net '$pwar!( . 0& ' #f#o
&ASCALS &RINCI&LE
#hat happens to a pressure in an enclosed 3uidN 0ince atoms in a 3uid
are free to move about they transmit the pressure to all parts of the 3uid
and to the walls of the container. Memarkably the pressure is transmitted
undiminished. This phenomenon is called &as)a#s 'rin)i'#e because it
was $rst clearly stated by the 'rench philosopher and scientist >laise
Qascal (*4;V*4)8A chan&e in pre$re applie! to an encloe! 4$i! i
tranmitte! $n!iminihe! to all portion of the 4$i! an! to the wall of it
container5
Qascals principle an experimentally veri$ed fact is what makes pressure
so important in 3uids. 0ince a change in pressure is transmitted
undiminished in an enclosed 3uid we often know more about pressure
than other physical quantities in 3uids. &oreover Qascals principle
implies that the total pressure in a 3uid is the sum of the pressures from
di"erent sources. #e shall $nd this fact2that pressures add2very useful.
7/26/2019 Compilation in Physics 212
54/113
DEFINITION OF TERMS
(Fluids)
Ar)2i+ees 'rin)i'#e the buoyant force on an ob-ect equals theweight of the 3uid it displaces
a,s!#u"e 'ressure the sum of gauge pressure and atmospheric
pressure
a2esive (!r)es the attractive forces between molecules of di"erent
types
,u!*an" (!r)e the net upward force on any ob-ect in any 3uid
)a'i##ar* a)"i!n the tendency of a 3uid to be raised or lowered in a
narrow tube
)!2esive (!r)es the attractive forces between molecules of thesame type
)!n"a)" ang#e the anglebetween the tangent to the liquid surface
and the surface
ensi"* the mass per unit volume of a substance or ob-ect
ias"!#i) 'ressure the minimum blood pressure in the artery
7/26/2019 Compilation in Physics 212
55/113
ias"!#i) 'ressure minimum arterial blood pressure1 indicator for
the 3uid balance
>uis liquids and gases1 a 3uid is a state of matter that yields to
shearing forces
gauge 'ressure the pressure relative to atmospheric pressure
g#au)!+a condition caused by the buildup of 3uid pressure in the
eye
in"ra!)u#ar 'ressure 3uid pressure in the eye
+i)"uri"i!n re>e stimulates the feeling of needing to urinate
triggered by bladder pressure
&as)a#s &rin)i'#e a change in pressure applied to an enclosed 3uid
is transmitted undiminished to all portions of the 3uid and to the walls
of itscontainer
'ressure the force per unit area perpendicular to the force over
which the force acts
'ressure the weight of the 3uid divided by the area supporting it
7/26/2019 Compilation in Physics 212
56/113
s'e)i-) gravi"* the ratio of the density of an ob-ect to a 3uid
(usually water)
sur(a)e "ensi!n the cohesive forces between molecules which cause
the surface of a liquid to contract to the smallest possible surface area
s*s"!#i) 'ressure the maximum blood pressure in the artery
s*s"!#i) 'ressure maximum arterial blood pressure1 indicator for the
blood 3ow
7/26/2019 Compilation in Physics 212
57/113
SOLVED &RO/LEMS
(Fluids)
*. The density of steel is /=
7/26/2019 Compilation in Physics 212
58/113
Solution:
Biven8 4
7/26/2019 Compilation in Physics 212
59/113
Mequired8 force that is exerted on the piston
'ormula8
F=*A
F=(300*a )(0.5m2 )
F=*A
F=150 (*a )m2
F=150N/m2 m2
F=150N (answer )
D. % manometer connected to a pipe indicates a negative gauge pressure
of
7/26/2019 Compilation in Physics 212
60/113
*atmosp3ere=1 1x105N/m2
*a/so2te=*'a2'e+*atmosp3eric
#'3+ *atmosp3eric
*;. x *
7/26/2019 Compilation in Physics 212
61/113
. % block of wood of mass ;. kg 3oats in water. alculate the buoyant
force on the block.
Solution:
Biven8 mass of ;. kg
Mequired8 buoyant force on the block
'ormula8The wooden block is 3oating so the buoyant force is equal to the
weight of the block or
F=m '
' (;. kg) (H.= m + s4)
' ;D.; 5 (answer )
/. % retaining wall m high and 4.m wide retains water up to its top. 'ind
the total pressure per meter length of the wall and the point at which
the resultant cuts the base. %lso $nd the resultant thrust on the base
of the wall per meter length. %ssume weight of masonry as 4; P5+m;.
Solution:
Biven8 m high4.m wideweight of masonry as 4; P5+m;
Mequired8 total pressure per meter length of the wallresultant thrust on the base of the wall per meter length
'ormula8
#e know that total pressure per meter length of the wall
7/26/2019 Compilation in Physics 212
62/113
Qoints at which the resultant cuts the base
#e also know that weight of masonry per meter length of the wall
and distance between the mid!point 'M(of the wall and the point
where resultant cuts the base '-(.
Mesultant thrust on the base of the wall per meter length
#e know that resultant thrust on the base of the wall per meter length
=. % pipe of cross sectional area =< cm4has a constriction where the area
is reduced to 4< cm4. If the velocity of the 3uid in the larger area is
7/26/2019 Compilation in Physics 212
63/113
Biven8 area =< cm41reduced to 4< cm4
velocity of the 3uid in the larger area is
7/26/2019 Compilation in Physics 212
64/113
.=m
#
.= 2k'
8700 k' /m3
.=2.299x104 m3
alculate the buoyant force8
F=#'.
F= (**
7/26/2019 Compilation in Physics 212
65/113
wt=m '
wt=(600k' )(9.8m/s2)
wt=5880N
7/26/2019 Compilation in Physics 212
66/113
Chapter 26 Ma&netim
DISCUSSION AND DERIVATION OFFORMULAS IN MAHNETISM Magne"s
Figure %%.3 &agnets come in various shapes si,es and strengths. %ll have
both a north pole and a south pole. There is never an isolated pole (a monopole).
%ll magnets attract iron such as that in a refrigerator door. Gowever
magnets may attract or repel other magnets. Experimentation shows that
all magnets have two poles. If freely suspended one pole will point toward
the north. The two poles are thus named the n!r"2 +agne"i) '!#e and
the s!u"2 +agne"i) '!#e (or more properly north!seeking and south!
seeking poles for the attractions in those directions).
7/26/2019 Compilation in Physics 212
67/113
Figure %%. Sne end of a bar magnet is suspended from a thread that
points toward north. The magnets two poles are labeled 5 and 0 for north!
seeking and south!seekingpoles respectively.
E#e)"r!+agne"s
7lectroma&net
Early in the *Hth century it was discovered that electrical currents cause
magnetic e"ects. The $rst signi$cant observation was by the Fanish
scientist Gans hristian Sersted (*///V*=*) who found that a compass
needle was de3ected by a current!carrying wire. This was the $rst
signi$cant evidence that the movement of charges had any connection with
magnets. E#e)"r!+agne"is+ is the use of electric current to make
magnets. These temporarily induced magnets are called e#e)"r!+agne"s.
Electromagnets are employed for everything from a wrecking yard crane
that lifts scrapped cars to controlling the beam of a H
particle accelerator to the magnets in medical imaging machines (0ee
Figure %%.4).
7/26/2019 Compilation in Physics 212
68/113
Figure %%.4 Instrument for magnetic resonance imaging (&MI). The
device uses a superconducting cylindrical coil for the main magnetic
$eld. The patient goes into this [tunnel\ on the gurney. (credit8 >ill
&chesney 'lickr)
Figure %%.10 showsthat the response of iron $lings to a current!
carrying coil and to a permanent bar magnet. The patterns are similar. In
fact electromagnets and ferromagnets have the same basic
characteristics2for example they have north and south poles that
cannot be separated and for which like poles repel and unlike poles
attract.
Figure %%.10 Iron $lings near (a) a current!carrying coil and (b) a
magnet act like tiny compass needles showing the shape of their $elds.
7/26/2019 Compilation in Physics 212
69/113
Their response to a current!carryingcoil and a permanent magnet is seen
to be very similar especially near the ends of the coil and the magnet.
Magne"i) Fie#s an Magne"i) Fie# Lines
Einstein is said to have been fascinated by a compass as a child
perhaps musing on how the needle felt a force without direct physical
contact. Gis ability to think deeply and clearly about action at a distance
particularly for gravitational electric and magnetic forces later enabled
him to create his revolutionary theory of relativity. 0ince magnetic forces
act at a distance we de$ne a +agne"i) -e# to represent magnetic
forces. The pictorial representation of +agne"i) -e# #ines is very
useful in visuali,ing the strength and direction of the magnetic $eld. %s
shown in Figure %%.15 the ire)"i!n !( +agne"i) -e# #ines is
de$ned to be the direction in which the north end of a compass needle
points. The magnetic $eld is traditionallycalled the B9-e#.
Figure %%.15 &agnetic $eld lines are de$ned to have the direction that
a small compass points when placed at a location. (a) If small compasses
are used to map themagnetic $eld around a bar magnet they will point
in the directions shown8 away from the north pole of the magnet toward
the south pole of the magnet. (Mecall that the Earths north magnetic
7/26/2019 Compilation in Physics 212
70/113
pole is really a south pole in terms of de$nitions of poles on a bar
magnet.) (b) onnecting the arrows gives continuous magnetic $eld
lines. The strength of the $eld is proportional to the closeness (or
density) of the lines. (c) If the interior of the magnet could be probed
the $eld lines would be found to form continuous closed loops.
0mall compasses used to test a magnetic $eld will not disturb it.
(This is analogous to the way we tested electric $elds with a small test
charge. In both cases the $elds represent only the ob-ect creating them
and not the probe testing them.) Figure %%.16 shows how the magnetic
$eld appears for a current loop and a long straight wire as could beexplored with small compasses. % small compass placed in these $elds
will align itself parallel to the $eld line at its location with its north pole
pointing in the direction of . 5ote the symbols used for $eld into and out
of the paper.
Figure %%.16 0mall compasses could be used to map the $elds shown here.
(a) The magnetic $eld of a circular current loop is similar to that of a bar
magnet. (b) % long andstraight wire creates a $eld with magnetic $eld lines
forming circular loops. (c) #hen the wire is in the plane of the paper the $eld
7/26/2019 Compilation in Physics 212
71/113
is perpendicular to the paper. 5ote that the symbols used for the $eld pointing
inward (like the tail of an arrow) and the $eld pointing outward (like the tip of
an arrow).
The strength of the $eld is proportional to the closeness of the lines. It is
exactly proportional to the number of lines per unit area perpendicular to
the lines (called the areal density).&agnetic $eld lines can never cross
meaning that the $eld is unique at any point in space. &agnetic $eld lines
are continuous forming closed loops without beginning or end. They go
from the north pole to the south pole. The last property is related to the fact
that the north and south poles cannot be separated. It is a distinct
di"erence from electric $eld lines which begin and end on the positive and
negative charges. If magnetic monopoles existed then magnetic $eld lines
would begin and end on them.
Magne"i) Fie# S"reng"2 F!r)e !n a M!ving C2arge in a
Magne"i) Fie#
#hat is the mechanism by which one magnet exerts a force onanotherN The answer is related to the fact that all magnetism is caused by
current the 3ow of charge. Ma&netic 8el! exert force on movin&
char&e and so they exert forces on other magnets all of which have
moving charges.
Right Hand Rule 1
The magnetic force on a moving charge is one of the most
fundamental known. &agnetic force is as important as the electrostatic or
oulomb force. Zet the magnetic force is more complex in both the number
7/26/2019 Compilation in Physics 212
72/113
of factors that a"ects it and in its direction than the relatively simple
oulomb force. The magnitude of the +agne"i) (!r)e 3 on a charge 9
moving at a speed vin a magnetic $eld of strength
3 9v sin (44.*)
where is the angle between the directions of vand /. This force is often
called the L!ren" (!r)e. In fact this is how we de$ne the magnetic $eld
strength 2in terms of the force on a charged particle moving in a
magnetic $eld. The 0I unit for magnetic $eld strength is called the "es#a
(T) after the eccentric but brilliant inventor 5ikola Tesla (*=V*HD;). To
determine how the tesla relates to other 0I units we solve 3 9vsin for
.
3 (44.4)
9v sin
>ecause sin is unitless the tesla is
* 5* T * 5
(44.;)
E ]
m+s
% ]
m
(note that +s %).
%nother smaller unit called the gauss (B) where * B *
7/26/2019 Compilation in Physics 212
73/113
superconducting electromagnets may attain *< T or more. The Earths
magnetic $eld on its surface is only about Y*
7/26/2019 Compilation in Physics 212
74/113
DEFINITION OF TERMS
(Magnetism)
De-ni"i!n !( Ter+s
B9-e#another term for magnetic $eld
A+'eres #a$ the physical law that states that the magnetic
$eld around an electric current is proportional to the current1each segment of currentproduces a magnetic $eld like that of a
long straight wire and the total $eld of any shape current is the
vector sum of the $elds due to each segment
/i!"9Savar" #a$ a physical law that describes the magnetic $eld
generated by an electric current in terms of a speci$c equation
Curie "e+'era"ure the temperature above which a ferromagnetic
material cannot be magneti,edire)"i!n !( +agne"i) -e# #ines
the direction that the north end of a compass needle points
!+ains regions within a material that behave like small bar
magnets
e#e)"r!+agne" an ob-ect that is temporarily magnetic when an
electrical current is passed through it e#e)"r!+agne"is+ the use
of electrical currents to induce magnetism
(err!+agne"i) materials such as iron
cobalt nickel and gadolinium thatexhibit strong magnetic e"ects gauss B
/D o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
75/113
the unit of the magnetic $eld strength1
* B *
7/26/2019 Compilation in Physics 212
76/113
+agne"ie to be turned into a magnet1 to be induced to be
magnetic
+agne"!)ari!gra+ :MCH; a recording of the hearts magnetic
$eld as it beats
+agne"!en)e'2a#!gra+ :MEH; a measurement of the brains
magnetic $eld
+e"er common application of magnetic torque on a current!
carrying loop that is very similar in construction to a motor1 by
design the torque isproportional to :and not so the needle
de3ection is proportional to the current
+!"!r loop of wire in a magnetic $eld1 when current is passed
through the loops the magnetic $eld exerts torque on the loopswhich rotates a shaft1 electrical energy is converted to
mechanical work in the process
n!r"2 +agne"i) '!#e the end or the side of a magnet that is
attracted toward Earths geographic north pole
nu)#ear +agne"i) res!nan)e :NMR; a phenomenon in which an
externally applied magnetic $eld interacts with the nuclei of certain
atoms
'er+ea,i#i"* !( (ree s'a)e the measure of the ability of a
material in this case free space to support a magnetic $eld1 the
constant
/ o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
77/113
o
7/26/2019 Compilation in Physics 212
78/113
SOLVED &RO/LEMS
(Magnetism)
1. If k.m+d4is equal to 5+%mp.m $nd the magnetic $eld produced by
them*and m4at point %.
%. 'ind the forces exerted by 0 poles of magnets given below.
/= o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
79/113
F
7/26/2019 Compilation in Physics 212
80/113
/3% and wires are given below. 'ind the magnetic $eld of % > and
at points ^ and Z.
Dire)"i!ns !( +agne"i) -e#s a" '!in" are (!un using rig2"
2an ru#e.
/A !u"$ar
//in$ar
=< o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
81/113
/Cin$ar
///J/C9/A
/%
7/26/2019 Compilation in Physics 212
82/113
Inu)e e+(9:;8:";.N
C2ange in F#u
%91
10 sin)e )r!ss se)"i!n area !( s!#en!i an +agne"i) -e#
#ines are 'ara##e# "! ea)2 !"2er.
%/.A
/.A90/.A
9/.A.N8"
6. 'ind the magnetic 3ux through a square with side of ; cm whichis located near a long straight conductor with electric current of
* %. Sne side of the square is parallel to the conductor with
distance of D cm between the side and the conductor. The opposite
side of the square is located cm away from the conductor.
a;cm
7/26/2019 Compilation in Physics 212
83/113
:*%
!*Dcm
7/26/2019 Compilation in Physics 212
84/113
`;i`
7/26/2019 Compilation in Physics 212
85/113
hange in 'lux1
4!*
*.%
>.%!.%
!>.%.5+t
4. % coil of wire of one turn has a cross!sectional area of = o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
86/113
1%. % solenoid has =< cm diameter number of loop is D and
magnetic $eld inside it is *4 .*
7/26/2019 Compilation in Physics 212
87/113
Chapter 2= 7lectrotatic
DISCUSSION AND DERIVATION OF
FORMULAS IN ELECTROSTATICSE#e)"ri) C2arge an E#e)"ri) Fie#
The image of %merican politician and scientist >en-amin 'ranklin
(*/
7/26/2019 Compilation in Physics 212
88/113
Figure 1B.% #hen >en-amin 'ranklin demonstrated that lightning was
related to static electricity he made a connection that is now part of the
evidence that all directlyexperienced forces except the gravitational force are
manifestations of the electromagnetic force.
&uch has been written about 'ranklin. Gis experiments were only
part of the life of a man who was a scientist inventor revolutionary
statesman and writer. 'ranklins experiments were not performed in
isolation nor were they the only ones to reveal connections.
'or example the Italian scientist Juigi Balvani (*/;/V*/H=) performed
a series of experiments in which static electricity was used to stimulate
contractions of leg muscles of dead frogs an e"ect already known in
humans sub-ected to static discharges. >ut Balvani also found that if he
-oined two metal wires (say copper and ,inc) end to end and touched the
other ends to muscles he produced the same e"ect in frogs as static
discharge. %lessandro olta (*/DV*=4/) partly inspired by Balvanis
work experimented with various combinations of metals and developed
the battery.
Furing the same era other scientists made progress in discovering
fundamental connections. The periodic table was developed as the
systematic properties of the elements were discovered. This in3uenced
the development and re$nement of the concept of atoms as the basis of
matter. 0uch submicroscopic descriptions of matter also help explain a
great deal more.
%tomic and molecular interactions such as the forces of friction
cohesion and adhesion are now known to be manifestations of thee#e)"r!+agne"i) (!r)e. 0tatic electricity is -ust one aspect of the
== o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
89/113
electromagnetic force which also includes moving electricity and
magnetism.
%ll the macroscopic forces that we experience directly such as the
sensations of touch and the tension in a rope are due to the
electromagnetic force one of the four fundamental forces in nature. The
gravitational force another fundamental force is actually sensed through
the electromagnetic interaction of molecules such as between those in
our feet and those on the top of a bathroom scale. (The other two
fundamental forces the strong nuclear force and the weak nuclear force
cannot be sensed on the human scale.)
This chapter begins the study of electromagnetic phenomena at a
fundamental level. The next several chapters will cover static electricity
moving electricity and magnetism2collectively known as
electromagnetism. In this chapter we begin with the study of electric
phenomena due to charges that are at least temporarily stationary
called electrostatics or static electricity.
S"a"i) E#e)"ri)i"* an C2arge C!nserva"i!n !( C2arge
#hat makes plastic wrap clingN 0tatic electricity. 5ot only are
applications of static electricity common these days its existence has
been known since ancient times. The $rst record of its e"ects dates to
ancient Breeks who noted more than .. that polishing amber
temporarily enabled it to attract bits of straw (see Figure 1B.3). The very
wordelectric
derives from the Breek word for amber (electron
).
=H o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
90/113
&any of the characteristics of static electricity can be explored by rubbing
things together. Mubbing creates the spark you get from walking across a
wool carpet for example. 0tatic cling generated in a clothes dryer and the
attraction of straw to recently polished amber also result from rubbing.
0imilarly lightning results from air movements under certain weather
conditions. Zou can also rub a balloon on your hair and the static
electricity created can then make the balloon cling to a wall. #e also have
to be cautious of static electricity especially in dry climates. #hen we
pump gasoline we are warned to discharge ourselves (after sliding across
the seat) on a metal surface before grabbing the gas no,,le. %ttendants in
hospital operating rooms must wear booties with aluminum foil on the
bottoms to avoid creating sparks which may ignite the oxygen being used.
0ome of the most basic characteristics of static electricity include8
The e"ects of static electricity are explained by a physical quantity not
previously introduced called electric charge.
There are only two types of charge one called positive and the other
called negative.
Jike charges repel whereas unlike charges attract.
The force between charges decreases with distance.
Gow do we know there are two types of e#e)"ri) )2argeN #hen
various materials are rubbed together in controlled ways certaincombinations of materials always produce one type of charge on one
H< o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
91/113
material and the opposite type on the other. >y convention we call
one type of charge [positive\ and the other type [negative.\ 'or
example when glass is rubbed with silk the glass becomes positively
charged and the silk negatively charged. 0ince the glass and silk haveopposite charges they attract one another like clothes that have
rubbed together in a dryer. Two glass rods rubbed with silk in this
manner will repel one another since each rod has positive charge on
it. 0imilarly two silk cloths so rubbed will repel since both cloths have
negative charge. Figure 1B. shows how these simple materials can
be used to explore the nature of the force between charges.
Figure 1B. % glass rod becomes positively charged when rubbed with silk
while the silk becomes negatively charged. (a) The glass rod is attracted to
the silk because theircharges are opposite. (b) Two similarly charged glass
rods repel. (c) Two similarly charged silk cloths repel.
E#e)"ri) Fie# C!n)e'" !( a Fie# Revisi"e
ontact forces such as between a baseball and a bat are explained
on the small scale by the interaction of the charges in atoms and
molecules in close proximity. They interact through forces that include
H* o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
92/113
the C!u#!+, (!r)e. %ction at a distance is a force between ob-ects that
are not close enough for their atoms to [touch.\ That is they are
separated by more than a few atomic diameters.
'or example a charged rubber comb attracts neutral bits of paper
from a distance via the oulomb force. It is very useful to think of an
ob-ect being surrounded in space by a (!r)e -e#. The force $eld carries
the force to another ob-ect (called a test ob-ect) some distance away.
C!n)e'" !( a Fie#
% $eld is a way of conceptuali,ing and mapping the force that
surrounds any ob-ect and acts on another ob-ect at a distance without
apparent physical connection. 'or example the gravitational $eldsurrounding the earth (and all other masses) represents the gravitational
force that would be experienced if another mass were placed at a given
point within the $eld.
Ear"2s E#e)"ri) Fie#
% near uniform electric $eld of approximately *< 5+ directed
downward surrounds Earth with the magnitude increasing slightly as we
get closer to the surface. #hat causes the electric $eldN %t around *
7/26/2019 Compilation in Physics 212
93/113
including the electric $eld surrounding Earth. In fair weather the
ionosphere is positive and the Earth largely negative maintaining the
electric $eld (Figure 1B.3(a)).
In storm conditions clouds form and locali,ed electric $elds can be
larger and reversed in direction (Figure 1B.3(b)). The exact charge
distributions depend on the local conditions and variations of Figure
1B.3(b) are possible.
If the electric $eld is su@ciently large the insulating properties of the
surrounding material break down and it becomes conducting. 'or air this
occurs at around ;Y*
7/26/2019 Compilation in Physics 212
94/113
0o far we have considered excess charges on a smooth symmetrical
conductor surface. #hat happens if a conductor has sharp corners or is
pointedN Excess charges on a non uniform conductor become
concentrated at the sharpest points. %dditionally excess charge may
move on or o" the conductor at the sharpest points.
To see how and why this happens consider the charged conductor in
Figure 1B.35. The electrostatic repulsion of like charges is most e"ective
in moving them apart on the 3attest surface and so they become least
concentrated there. This is because the forces between identical pairs of
charges at either end of the conductor are identical but the components
of the forces parallel to the surfaces are di"erent. The component parallel
to the surface is greatest on the 3attest surface and hence more
e"ective in moving the charge.
The same e"ect is produced on a conductor by an externally applied
electric $eld as seen in Figure 1B.35 (c). 0ince the $eld lines must be
perpendicular to the surface more of them are concentrated on the most
curved parts.
A''#i)a"i!ns !( C!nu)"!rs
Sn a very sharply curved surface such as shown in Figure 1B.36 the
charges are so concentrated at the point that the resulting electric $eld
can be great enough to remove them from the surface. This can be useful.
HD o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
95/113
Jightning rods work best when they are most pointed. The large charges
created in storm clouds induce an opposite charge on a building that can
result in a lightning bolt hitting the building. The induced charge is bled
away continually by a lightning rod preventing the more dramatic
lightning strike.
Sf course we sometimes wish to prevent the transfer of charge rather
than to facilitate it. In that case the conductor should be very smooth and
have as large a radius of curvature as possible. (0ee Figure 1B.37.)
0mooth surfaces are used on high!voltage transmission lines for example
to avoid leakage of charge into the air.
%nother device that makes use of some of these principles is a Faraa*
)age. This is a metal shield that encloses a volume. %ll electrical charges
will reside on the outside surface of this shield and there will be no
electrical $eld inside.
% 'araday cage is used to prohibit stray electrical $elds in the
environment from interfering with sensitive measurements such as
the electrical signals inside a nerve cell.
Furing electrical storms if you are driving a car it is best to stay
inside the car as its metal body acts as a 'araday cage with ,ero
electrical $eld inside. If in the vicinity of a lightning strike its e"ect
is felt on the outside of the car and the inside is una"ected provided
you remain totally inside. This is also true if an active ([hot\)
H o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
96/113
electrical wire was broken (in a storm or an accident) and fell on
your car.
Figure 1B.36 % very pointed conductor has a large charge concentration at the
point. The electric $eld is very strong at the point and can exert a force large
enough to transfer charge on or o" the conductor. Jightning rods are used to
prevent the buildup of large excess charges on structures and thus are pointed.
C!nu)"!rs an Insu#a"!rs
Qolari,ation is the separation of positive and negative charges in a neutral
ob-ect.
H o m p I l a t I o n I n Q h y s I c s 4 * 4
http://var/www/apps/conversion/tmp/scratch_4/HYPERLINK%23page635http://var/www/apps/conversion/tmp/scratch_4/HYPERLINK%23page6357/26/2019 Compilation in Physics 212
97/113
% conductor is a substance that allows charge to 3ow freely through its
atomic structure.
%n insulator holds charge within its atomic structure.
Sb-ects with like charges repel each other while those with unlike charges
attract each other.
% conducting ob-ect is said to be grounded if it is connected to the
Earth through a conductor. Brounding allows transfer of charge to and
from the earths large reservoir.
Sb-ects can be charged by contact with another charged ob-ect and obtain
the same sign charge.
If an ob-ect is temporarily grounded it can be charged by induction and
obtains the opposite sign charge.
Qolari,ed ob-ects have their positive and negative charges concentrated in
di"erent areas giving them a non!symmetrical charge.
Qolar molecules have an inherent separation of charge.
C!u#!+,s La$
H/ o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
98/113
'renchman harles oulomb was the $rst to publish the mathematical
equation that describes the electrostatic force between two ob-ects.
oulombs law gives the magnitude of the force between point charges. It
is
where 9*and 94are two point charges separated by a distance r and k
H.
7/26/2019 Compilation in Physics 212
99/113
The electrostatic force $eld surrounding a charged ob-ect extends out into
space in all directions.
The electrostatic force exerted by a point charge on a test charge at a
distance r depends on the charge of both charges as well as the
distance between the two.
The electric $eld Eis de$ned to be
E 9,F
where Fis the oulomb or electrostatic force exerted on a small positivetest charge 9. Ehas units of 5+.
The magnitude of the electric $eld Ecreated by a point charge >is
E k`r>4`.
where ris the distance from >. The electric $eld Eis a vector and $elds
due to multiple charges add like vectors.
E#e)"ri) Fie# Lines Mu#"i'#e C2arges
Frawings of electric $eld lines are useful visual tools. The properties of
electric $eld lines for any charge distribution are that8
'ield lines must begin on positive charges and terminate on negative
charges or at in$nity in the hypothetical case of isolated charges.
The number of $eld lines leaving a positive charge or entering a negative
charge is proportional to the magnitude of the charge.
HH o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
100/113
The strength of the $eld is proportional to the closeness of the $eld lines
2more precisely it is proportional to the number of lines per unit area
perpendicular to the lines.
The direction of the electric $eld is tangent to the $eld line at any point in
space.
'ield lines can never cross.
E#e)"ri) F!r)es in /i!#!g*
&any molecules in living organisms such as F5% carry a charge.
%n uneven distribution of the positive and negative charges within a polar
molecule produces a dipole.
The e"ect of a oulomb $eld generated by a charged ob-ect may be
reduced or blocked by other nearby charged ob-ects.
>iological systems contain water and because water molecules are polar
they have a strong e"ect on other molecules in living systems.
*
7/26/2019 Compilation in Physics 212
101/113
C!nu)"!rs an E#e)"ri) Fie#s in S"a"i) Eui#i,riu+
% conductor allows free charges to move about within it.
The electrical forces around a conductor will cause free charges to move
around inside the conductor until static equilibrium is reached.
%ny excess charge will collect along the surface of a conductor.
onductors with sharp corners or points will collect more charge at those
points.
% lightning rod is a conductor with sharply pointed ends that collect
excess charge on the building caused by an electrical storm and allow it
to dissipate back into the air.
Electrical storms result when the electrical $eld of Earths surface in
certain locations becomes more strongly charged due to changes in the
insulating e"ect of the air.
% 'araday cage acts like a shield around an ob-ect preventing electric
charge from penetrating inside.
*
7/26/2019 Compilation in Physics 212
102/113
A''#i)a"i!ns !( E#e)"r!s"a"i)s
Electrostatics is the study of electric $elds in static equilibrium.
In addition to research using equipment such as a an de Braa"
generator many practical applications of electrostatics exist
including photocopiers laser printers ink!-et printers and electrostatic
air $lters.
DEFINITION OF TERMS
(Magnetism)
De-ni"i!n !( Ter+s
a+'#i"ue +!u#a"i!n :AM; a method for placing information on
electromagnetic waves by modulating the amplitude of a carrier
wave with an audio signal resulting in a wave with constant
frequency but varying amplitude
*
7/26/2019 Compilation in Physics 212
103/113
a+'#i"ue the height or magnitude of an electromagnetic wave
)arrier $ave an electromagnetic wave that carries a signal by
modulation of its amplitude or frequency
e#e)"ri) -e# #ines a pattern of imaginary lines that extend
between an electric source and charged ob-ects in the surrounding
area with arrowspointed away from positively charged ob-ects and
toward negatively charged ob-ects. The more lines in the pattern the
stronger the electric $eld in that region
e#e)"ri) -e# s"reng"2 the magnitude of the electric $eld denoted
7!$eld
e#e)"ri) -e# a vector quantity (E)1 the lines of electric force per
unit charge moving radially outward from a positive charge and intoward anegative charge
e#e)"r!+agne"i) s'e)"ru+ the full range of wavelengths or
frequencies of electromagnetic radiation
e#e)"r!+agne"i) $aves radiation in the form of waves of electric
and magnetic energy
e#e)"r!+!"ive (!r)e :e+(; energy produced per unit charge
drawn from a source that produces an electrical current
e"re+e#* #!$ (reuen)* :ELF; electromagnetic radiation with
wavelengths usually in the range of < to ;
7/26/2019 Compilation in Physics 212
104/113
(reuen)* +!u#a"i!n :FM; a method of placing information on
electromagnetic waves by modulating the frequency of a carrier
wave with anaudio signal producing a wave of constant amplitude
but varying frequency
(reuen)* the number of complete wave cycles (up!down!up)
passing a given point within one second (cycles+second)
ga++a ra* ( ray)1 extremely high frequency electromagnetic
radiation emitted by the nucleus of an atom either from naturalnuclear decay or induced nuclear processes in nuclear reactors and
weapons. The lower end of the !ray frequency range overlaps the
upper end of the ^!ray range but rays can have the highest
frequency of any electromagnetic radiation
2er" an 0I unit denoting the frequency of an electromagnetic
wave in cycles per second
in(rare raia"i!n :IR; a region of the electromagnetic spectrum
with a frequency range that extends from -ust below the red region
of the visible light spectrum up to the microwave region or from
7/26/2019 Compilation in Physics 212
105/113
+agne"i) -e# s"reng"2 the magnitude of the magnetic $eld
denoted!$eld
+agne"i) -e# a vector quantity (/)1 can be used to determine the
magnetic force on a moving charged particle
+ai+u+ -e# s"reng"2 the maximum amplitude an
electromagnetic wave can reach representing the maximum amount
of electric force and+ormagnetic 3ux that the wave can exert
+i)r!$aves electromagnetic waves with wavelengths in the range
from * mm to * m1 they can be produced by currents in macroscopic
circuitsand devices
!s)i##a"e to 3uctuate back and forth in a steady beat
RLC )ir)ui" an electric circuit that includes a resistor capacitor and
inductor
raar a common application of microwaves. Madar can determine
the distance to ob-ects as diverse as clouds and aircraft as well as
determinethe speed of a car or the intensity of a rainstorm rai! $aves electromagnetic waves with wavelengths in the range
from * mm to *
7/26/2019 Compilation in Physics 212
106/113
in a vacuum such as space the speed of light is a
constant ; x *
7/26/2019 Compilation in Physics 212
107/113
9ra* invisible penetrating form of very high frequency
electromagnetic radiation overlapping both the ultraviolet range and
the
C!u#!+, (!r)eanother term for the electrostatic force
C!u#!+, in"era)"i!n the interaction between two charged
particles generated by the oulomb forces they exert on one another
C!u#!+,s #a$ the mathematical equation calculating the
electrostatic force vector between two charged particles conductor8 a
material that allows electrons to move separately from their atomic
orbits
)!nu)"!ran ob-ect with properties that allow charges to move
about freely within it
i'!#ea molecules lack of symmetrical charge distribution causing
one side to be more positive and another to be more negative
e#e)"ri) )2argea physical property of an ob-ect that causes it to
be attracted toward or repelled from another charged ob-ect1 each
charged ob-ect generates and is in3uenced by a force called an
electromagnetic force
e#e)"ri) -e# #inesa series of lines drawn from a point charge
representing the magnitude and direction of force exerted by that
charge electric $eld8 a three!dimensional map of the electric force
extended out into space from a point charge
e#e)"r!+agne"i) (!r)e one of the four fundamental forces of
nature1 the electromagnetic force consists of static electricity
moving electricity and magnetism
e#e)"r!n a particle orbiting the nucleus of an atom and carrying the
smallest unit of negative charge
e#e)"r!s"a"i) eui#i,riu+ an electrostatically balanced state inwhich all free electrical charges have stopped moving about
*
7/26/2019 Compilation in Physics 212
108/113
electrostatic force8 the amount and direction of attraction or
repulsion between two charged bodies
e#e)"r!s"a"i) 're)i'i"a"!rs$lters that apply charges to particles
in the air then attract those charges to a $lter removing them from
the airstream electrostatic repulsion8 the phenomenon of two ob-ects
with like charges repelling each other
e#e)"r!s"a"i)sthe study of electric forces that are static or slow!
moving
Faraa* )agea metal shield which prevents electric charge from
penetrating its surface
-e#a map of the amount and direction of a force acting on other
ob-ects extending out into space
(ree )2argean electrical charge (either positive or negative) which
can move about separately from its base molecule
(ree e#e)"r!nan electron that is free to move away from its atomic
orbit
gr!unewhen a conductor is connected to the Earth allowing
charge to freely 3ow to and from Earths unlimited reservoir
grounded8 connected to the ground with a conductor so that charge
3ows freely to and from the Earth to the grounded ob-ect induction8
the process by which an electrically charged ob-ect brought near a
neutral ob-ect creates a charge in that ob-ect
in
7/26/2019 Compilation in Physics 212
109/113
#aser 'rin"eruses a laser to create a photoconductive image on a
drum which attracts dry ink particles that are then rolled onto a
sheet of paper to print a high!quality copy of the image
#a$ !( )!nserva"i!n !( )2argestates that whenever a charge is
created an equal amount of charge with the opposite sign is created
simultaneously
'2!"!)!nu)"!ra substance that is an insulator until it is exposed
to light when it becomes a conductor point charge8 % charged
particle designated generating an electric $eld
'!#ar +!#e)u#e8 a molecule with an asymmetrical distribution of
positive and negative charge polari,ation8 slight shifting of positive
and negative charges to opposite sides of an atom or molecule
'!#arie a state in which the positive and negative charges within
an ob-ect have collected in separate locations
'r!"!na particle in the nucleus of an atom and carrying a positive
charge equal in magnitude and opposite in sign to the amount of
negative charge carried by an electron
s)reening the dilution or blocking of an electrostatic force on a
charged ob-ect by the presence of other charges nearby static
electricity8 a buildup of electric charge on the surface of an ob-ect
"es" )2arge8 % particle (designated q ) with either a positive or
negative charge set down within an electric $eld generated by a
point charge
Van e Hraa= genera"!r8 a machine that produces a large amount
of excess charge used for experiments with high voltage vector
addition8 mathematical combination of two or more vectors
including their magnitudes directions and positions vector8 aquantity with both magnitude and direction
*
7/26/2019 Compilation in Physics 212
110/113
er!gra'2*8 a dry copying process based on electrostatics
)a'a)i"an)e amount of charge stored per unit volt capacitor8 a
device that stores electric charge
e-,ri##a"!ra machine used to provide an electrical shock to a
heart attack victim6s heart in order to restore the heart6s normal
rhythmic pattern dielectric strength8 the maximum electric $eld
above which an insulating material begins to break down and
conduct
ie#e)"ri)an insulating material
e#e)"ri) '!"en"ia#potential energy per unit charge
e#e)"r!n v!#" the energy given to a fundamental charge
accelerated through a potential di"erence of one volt equipotential
line8 a line along which the electric potential is constant
gr!uning$xing a conductor at ,ero volts by connecting it to the
earth or ground
+e)2ani)a# energ*8 sum of the kinetic energy and potential energy
of a system1 this sum is a constant
'ara##e# '#a"e )a'a)i"!r8 two identical conducting plates separated
by a distance
'!#ar +!#e)u#ea molecule with inherent separation of charge
'!"en"ia# i=eren)e :!r v!#"age;change in potential energy of a
charge moved from one point to another divided by the charge1
units of potential di"erence are -oules per coulomb known as volt
s)a#arphysical quantity with magnitude but no direction
ve)"!rphysical quantity with both magnitude and direction
**< o m p I l a t I o n I n Q h y s I c s 4 * 4
7/26/2019 Compilation in Physics 212
111/113
AC )urren"8 current that 3uctuates sinusoidally with time expressed
as I I< sin 4Aft where I is the current at time t I< is the peak
current and f is the frequency in hert,
AC v!#"age8 voltage that 3uctuates sinusoidally with time
expressed as < sin 4Aft where is the voltage at time t < is
the peak voltage and f is the frequency in hert,
a#"erna"ing )urren"8 (%) the 3ow of electric charge that
periodically reverses direction
a+'ere(amp) the 0I unit for current1 * % * +s
,i!e#e)"ri)i"* electrical e"ects in and created by biological
systems direct current8 (F) the 3ow of electric charge in only one
direction
ri(" ve#!)i"*8 the average velocity at which free charges 3ow in
response to an electric $eld electric current8 the rate at which charge
3ows I +t
e#e)"ri) '!$er8 the rate at which electrical energy is su