Waves and Vibration

8/16/2019 Waves and Vibration

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Waves are everywhere in nature

Sound waves,visible lightwaves,radio waves,microwaves,water waves,

sine waves,

telephone chordwaves,stadium waves,earthquakewaves,waves on a

string,slinky waves


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What is a wave?

a wave is a disturbance that travelsthrough a medium from one location toanother.a wave is the motion of a disturbance


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Slinky Wave

Let’s use a slinky wave as an example.When the slinky is stretched from end to end

and is held at rest, it assumes a natural position known as the equilibrium or rest position .To introduce a wave here we must first createa disturbance.We must move a particle away from its rest

position.


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Slinky Wave

One way to do this is to erk the slinky forward the beginning of the slinky moves away from its

e!uilibrium position and then back.the disturbance continues down the slinky.this disturbance that moves down the slinky is

called a pulse .if we keep "pulsing# the slinky back and forth,we could get a repeating disturbance.


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Slinky WaveThis disturbance would look something like this

This type of wave is called a LO$%&T'(&$)L wave.The pulse is transferred through the medium of the slinky,but the slinky itself does not actually move.

&t ust displaces from its rest position and then returns to it.*o what really is being transferred+


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Slinky Wave

nergy is being transferred .The metal of the slinky is the - (&'- in that

transfers the energy pulse of the wave.The medium ends up in the same place as it

started it ust gets disturbed and then returnsto it rest position .The same can be seen with a stadium wave.


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Lon itudinal Wave

The wave we see here is a longitudinal wave.

The medium particles vibrate parallel to themotion of the pulse .This is the same type of wave that we use to

transfer sound./an you figure out how++

show tuning fork demo


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"ransverse waves

) second type of wave is a transversewave.We said in a longitudinal wave the pulsetravels in a direction parallel to thedisturbance.

&n a transverse wave the pulse travels perpendicular to the disturbance .


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"ransverse Waves

The differences between the two can be seen


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"ransverse Waves

Transverse waves occur when we wigglethe slinky back and forth.

They also occur when the sourcedisturbance follows a periodic motion. ) spring or a pendulum can accomplish

this.The wave formed here is a *&$ wave.http011webphysics.davidson.edu1course2material1py3451demo1illustration3627.html

http://webphysics.davidson.edu/course_material/py130/demo/illustration16_2.htmlhttp://webphysics.davidson.edu/course_material/py130/demo/illustration16_2.htmlhttp://webphysics.davidson.edu/course_material/py130/demo/illustration16_2.htmlhttp://webphysics.davidson.edu/course_material/py130/demo/illustration16_2.html


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$nato%y o& a Wave

$ow we can begin to describe theanatomy of our waves.We will use a transverse wave to describethis since it is easier to see the pieces.


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$nato%y o& a Wave

In our wave here the dashed line represents theequilibrium position.Once the medium is disturbed, it moves awayfrom this position and then returns to it


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$nato%y o& a Wave

The points ) and 8 are called the /9 *T*

of the wave.This is the point where the wave exhibits themaximum amount of positive or upwardsdisplacement

'rest


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$nato%y o& a Wave

The points ( and & are called the

T9O'%:* of the wave.These are the points where the waveexhibits its maximum negative or downwarddisplacement.

trou h


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$nato%y o& a Wave

The distance between the dashed line and

point ) is called the )mplitude of the wave.;This is the maximum displacement that thewave moves away from its e!uilibrium.

$%(litude


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$nato%y o& a Wave

The distance between two consecutive similar pointsetween what other points is can a wavelength bemeasured+

wavelen th


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$nato%y o& a WaveWhat else can we determine+We know that things that repeat have a

fre!uency and a period. :ow could we finda fre!uency and a period of a wave+


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Wave &re)uen'y

We know that fre!uency measure howoften something happens over a certain

amount of time.We can measure how many times a pulse

passes a fixed point over a given amount

of time, and this will give us the fre!uency.


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Wave &re)uen'y

*uppose & wiggle a slinky back and forth,and count that 6 waves pass a point in 7

seconds. What would the fre!uency be+4 cycles 1 second 4 :?

we use the term :ert?


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Wave *eriod

The period describes the same thing as itdid with a pendulum.

&t is the time it takes for one cycle tocomplete. &t also is the reciprocal of the fre!uency.

T @ 3 1 f f @ 3 1 T let’s see if you get it .

http://waves2.htm/http://waves2.htm/


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Wave S(eed

We can use what we know to determinehow fast a wave is moving.

What is the formula for velocity+velocity @ distance 1 time

What distance do we know about a wave

wavelengthand what time do we know

period


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Wave S(eed

so if we plug these in we get velocity @

length of pulse 1time for pulse to move pass a fixed point

v @λ 1 T

we will use the symbol λ to representwavelength


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Wave S(eed

v @λ 1 T but what does T e!ual

T @ 3 1 f so we can also write

v @ fλ

velocity @ fre!uency A wavelengthThis is known as the wave e!uation .examples



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Wave +ehavior

$ow we know all about waves. :ow to describe them, measure them andanaly?e them. >ut how do they interact+


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Wave +ehavior

We know that waves travel throughmediums.

>ut what happens when that medium runsout+


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+oundary +ehavior

The behavior of a wave when it reachesthe end of its medium is called the wave’s

>O'$()9B > :)C&O9 .When one medium ends and anotherbegins, that is called a boundary .


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,i-ed .nd

One type of boundary that a wave mayencounter is that it may be attached to a

fixed end . &n this case, the end of the medium willnot be able to move.

What is going to happen if a wave pulse goes down this string and encounters the fixed end+


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,i-ed .nd

:ere the incident pulse is an upward pulse.

The reflected pulse is upsideDdown. &t isinverted.The reflected pulse has the same speed ,wavelength , and amplitude as theincident pulse.


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,i-ed .nd $ni%ation


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,ree .nd

)nother boundary type is when a wave’smedium is attached to a stationary ob ect

as a free end . &n this situation, the end of the medium isallowed to slide up and down.

What would happen in this case+


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,ree .nd

:ere the reflected pulse is not inverted. &t is identical to the incident pulse, exceptit is moving in the opposite direction.The speed , wavelength , and amplitude are the same as the incident pulse.


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,ree .nd $ni%ation


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/han e in 0ediu%

Our third boundary condition is when themedium of a wave changes.

Think of a thin rope attached to a thinrope. The point where the two ropes areattached is the boundary.

)t this point, a wave pulse will transfer from one medium to another.What will happen here+


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/han e in 0ediu%

&n this situation part of the wave is reflected,and part of the wave is transmitted.

Eart of the wave energy is transferred to the

more dense medium, and part is reflected.The transmitted pulse is upright, while thereflected pulse is inverted.


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/han e in 0ediu%

The speed and wavelength of thereflected wave remain the same, but theamplitude decreases.

The speed , wavelength , and amplitude ofthe transmitted pulse are all smaller thanin the incident pulse.


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/han e in 0ediu% $ni%ation

"est your understandin



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Wave ntera'tion

)ll we have left to discover is how wavesinteract with each other.

When two waves meet while travelingalong the same medium it is called

&$T 98 9 $/ .


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/onstru'tive nter&eren'e

Let’s consider two waves moving towardseach other, both having a positive upward

amplitude.What will happen when they meet+


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/onstru'tive nter&eren'eThey will )(( together to produce a

greater amplitude.This is known as /O$*T9'/T&C

&$T 98 9 $/ .


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estru'tive nter&eren'e

$ow let’s consider the opposite, twowaves moving towards each other, one

having a positive


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estru'tive nter&eren'eThis time when they add together theywill produce a smaller amplitude.This is know as ( *T9'/T&C

&$T 98 9 $/ .


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/he'k our nderstandin

Which points will produce constructive interference andwhich will produce destructive interference +

/onstructive%, F, -, $

(estructive :, &, G, L, O

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Waves and Vibration