Umm Al-Qura University Dr. Abdulsalam Ali LECTURE …

LECTURE OUTLINE

CHAPTER 14

Waves and

1Umm Al-Qura University Dr. Abdulsalam Ali

Waves and

Sound

14-1 Types of Waves

� A wave:

Is a disturbance that propagates from one place

to another.

� 1- Transverse Wave:

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Umm Al-Qura University Dr. Abdulsalam Ali

� 1- Transverse Wave:

The displacement of the medium is perpendicular

to the direction of motion of the wave.

14-1 Types of Waves

� The wave on a string have the shape of sine or a

cosine; we call such a wave as a harmonic wave.

� The wave travels in the horizontal direction even

though your hand oscillates vertically about one

spot.

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spot.

� Ex: light and radio waves

14-1 Types of Waves

� Longitudinal Wave:

The displacement of individual particles is parallel

to the direction of propagation of the wave.

4

� Individual

particle in the

air oscillate back

and forth about

a given position


14-1 Types of Waves

� 3-Water Wave:

� Water waves are a

combination of

transverse and

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transverse and

longitudinal waves.

14-1 Types of Waves

� Period T:

time for one wavelength

to pass a given point

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� Wavelength λ:

distance over which wave

repeats

Distance m


14-1 Types of Waves

� Frequency:

� Number of oscillation per unit time.

7


14-1 Types of Waves

� Ex1:

8


14-1 Types of Waves

� Ex2:

9


14-1 Types of Waves

� Speed of Wave:

� The speed of the Waves determined by the

properties of the material through which they travel

10


14-1 Types of Waves11


14-3 Harmonic Wave Functions


12

� Since the wave has the same pattern at x + λ as it

does at x, the wave must be of the form

λ

X



13

� Also, as the wave propagates

in time, the peak moves as

tx

Tλ=

� And we can write

xT

λ=

(0)t

x xT

λ= −



14

� Combining yields the full

wave equation:

14-3 Harmonic Wave Functions15


� (a) 15 cm (d) 0.42

� (b) 10 cm (e) to the right

� (c) 24 s

14-2 Waves on a String

� For a string, the wave speed is determined by:

1. The tension in the string (F)

2. The mass of the string.

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� As the tension in the string increases, the speed of

waves on the string increases.



� A heavy string responds slowly to a given

disturbance because of its inertia.

� What is important is the mass of the string per

length µ

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� The speed ( ) of the wave on string increase with

tension (F) and decrease with the mass per length µν


14-2 Waves on a String18


14-2 Waves on a String19



� Reflections.

� When a wave reaches the end of a string, it will be

reflected. If the end is fixed, the reflected wave will

be inverted.

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be inverted.



� If the end of the string is free to move transversely,

the wave will be reflected without inversion.

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14-4 Sound Waves

� Sound waves are longitudinal waves.

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� Here, the wave is a series of compressions and

stretches.Umm Al-Qura University Dr. Abdulsalam Ali

14-4 Sound Waves

� In a sound wave, the

density and pressure of

the air (or other medium

carrying the sound) are

the quantities that

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the quantities that

oscillate.


14-4 Sound Waves

� The speed of sound in air at room temperature

= 343 m/s

20o c

υ

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� as air is heated the molecules will move faster, and hence the speed of sound will increase.

� The speed of sound is different in different materials; in general, the denser the material, the faster sound travels through it.


14-4 Sound Waves25


14-4 Sound Waves

Answer:

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14-4 Sound Waves

� The frequency of a Sound wave.

� Sound waves can have any frequency; the human

ear can hear sounds between about 20 Hz and

20,000 Hz.

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20,000 Hz.

� Sounds with frequencies greater than 20,000 Hz

are called ultrasonic; sounds with frequencies less

than 20 Hz are called infrasonic.


14-4 Sound Waves

� Ultrasonic waves are familiar from medical

applications. (Imaging and therapy).

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14-4 Sound Waves

� elephants and whales communicate, in part, by

infrasonic waves. Bats navigate in the dark by

ultrasonic sounds.

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14-4 Sound Waves

� It should be noted, that the speed of the sound is

the same for all frequencies.

fυ λ=

30

� For example if the frequency of a wave is doubled,

its wavelength is halved, so that speed stay the

same.

fυ λ=


14-5 Sound Intensity

� The loudness of a sound is determined by its intensity.

� The intensity of a sound is the amount of energy that

passes through a given area in a given time.

31


� Where : intensity,

� E :wave energy

� A :area

� t : time

I


� But the Power

� SI unit is watt ( W )EP

t=

32

� So



� The intensity of the sound decrease as we move

away from the source. The reason for this reduction

in intensity because the energy of sound spread out

over a large area.

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� So

24

PI

rπ=

22 1

21 2

I r

I r=


� Sound intensity from a point source will decrease as

the square of the distance.

34

2

12 1

2

rI I

r

=


14-5 Sound Intensity35



� Intensity level and Decibels.

� When you listen to a variety of sounds, a sound that

seems twice as loud as another is ten times more

intense.

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intense.

� Loudness is measured by the intensity level of a

wave.

� The quantity is called a (bel) ; a more common

unit is the decibel, (dB), which is a tenth of a bel.

β

β



� where, I0is the faintest

sound that can be heard:

37


0

sound that can be heard:

� The loudness of a sound

doubles with each

increase in intensity level

of 10 dB.

14-5 Sound Intensity38


14-7 Superposition and Interference

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� Superposition:

The combination of two or more waves to form a

result wave.

� Waves of small amplitude traveling through the


� Waves of small amplitude traveling through the

same medium combine, or superpose, by simple

addition.


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� 1- constructive interference

If two pulses combine to give a larger pulse, (a).

� 2- destructive interference

If two pulses combine to give a smaller pulse, (b).


If two pulses combine to give a smaller pulse, (b).


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� 1- constructive interference 2- destructive interference

- in Phase - opposite phase

3


1

2

3


� If the sources are in phase:

� Constructive interference occurs when the distance

to the sources differs by

� Destructive interference occurs when the distance to

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0,1 ,2 ,3 .......λ λ λ� Destructive interference occurs when the distance to

the sources differs by

1 3 5, , .......

2 2 2λ λ λ



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� If the sources have Opposite Phase:

� Constructive interference occurs when the distance

to the sources differs by 1 3 5, , .......

2 2 2λ λ λ

� Destructive interference occurs when the distance to

the sources differs by

0,1 ,2 ,3 .......λ λ λ

2 2 2



44



45


14-8 Standing Waves46

� A standing wave:

� Is the wave that fixed in its

location but oscillates with

time.time.

� These waves are found on

strings with both ends fixed,

such as in a musical

instrument; And also in

vibrating columns of air.



� 1- The fundamental, or lowest, frequency on a fixed

string has a wavelength twice the length of the

string. 1 1

12

2L Lλ λ= → =

� But the speed of the wave.

� So

2

1 1fυ λ=

11 2

fL

υ υλ

= =Umm Al-Qura University Dr. Abdulsalam Ali


� There must be an integral number of half-wavelengths

on the string; this means that only certain frequencies

are possible.

� Higher frequencies are called harmonics.


� Higher frequencies are called harmonics.

� Points on the string which never move are called nodes

(N); those which have the maximum movement are

called antinodes (A).






� Vibrating columns of air:

� Standing waves can also

be excited in columns of

air, such as soda bottles.air, such as soda bottles.

� As indicated in the

drawing, one end is a

node (N), and the other

is an antinode (A).



� In this case, the fundamental

wavelength is four times the

length of the pipe.

1

� So

14

4L Lλ λ= → =

11 4

fL

υ υλ

= =



� only odd-numbered harmonics appear.

� First harmonic ( fundamental )

� Third harmonic

� Fifth harmonic� Fifth harmonic

……. And so on.





� If the tube is open at both ends, both ends are

antinodes, and the sequence of harmonics is the

same as that on a string.


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Umm Al-Qura University Dr. Abdulsalam Ali LECTURE …