1. Chapter 16
Waves and Sound

2. A wave is a traveling disturbance.
16.1 The Nature of Waves
A wave is a traveling disturbance.
A wave carries energy from place to place.

3. 16.1 The Nature of Waves
Longitudinal Wave

4. 16.1 The Nature of Waves
Transverse Wave

5. over again by the source.
16.2 Periodic Waves
Periodic waves consist of cycles or patterns that are produced over and
over again by the source.
In the figures, every segment of the slinky vibrates in simple harmonic
motion, provided the end of the slinky is moved in simple harmonic
motion.

6. In the drawing, one cycle is shaded in color.
16.2 Periodic Waves
In the drawing, one cycle is shaded in color.
The amplitude A is the maximum excursion of a particle of the medium from
the particles undisturbed position.
The wavelength is the horizontal length of one cycle of the wave.
The period is the time required for one complete cycle.
The frequency is related to the period and has units of Hz, or s-1.

7. Example 1 The Wavelengths of Radio Waves
16.2 Periodic Waves
Example 1 The Wavelengths of Radio Waves
AM and FM radio waves are transverse waves consisting of electric and
magnetic field disturbances traveling at a speed of 3.00x108m/s. A station
broadcasts AM radio waves whose frequency is 1230x103Hz and an FM
radio wave whose frequency is 91.9x106Hz. Find the distance between
adjacent crests in each wave.

8. 16.2 Periodic Waves AM FM

9. 16.3 The Speed of a Wave on a String
The speed at which the wave moves to the right depends on how quickly
one particle of the string is accelerated upward in response to the net
pulling force.
tension
linear density
file:///Users/silvinagatica/Desktop/class/simulations/applets/sim24.htm

10. 16.3 The Speed of a Wave on a String
Example 2 Waves Traveling on Guitar Strings
Transverse waves travel on each string of an electric guitar after the
string is plucked. The length of each string between its two fixed ends
is m, and the mass is g for the highest pitched E string and
3.32 g for the lowest pitched E string. Each string is under a tension
of 226 N. Find the speeds of the waves on the two strings.

11. 16.3 The Speed of a Wave on a String
High E
Low E

12. 16.3 The Speed of a Wave on a String
Conceptual Example 3 Wave Speed Versus Particle Speed
Is the speed of a transverse wave on a string the same as the speed at
which a particle on the string moves?

13. 16.4 The Mathematical Description of a Wave
phase: Φ (in radians)
Interpretation of the formula:
y=0 for Φ=0
This happens for:
x represents the position of a point traveling with speed v, to the right
After t=T, x moved to

14. 16.4 The Mathematical Description of a Wave
y=0 for Φ= 0
This happens for:
This is the position of a point traveling with speed v, to the left

15. 16.4 The Mathematical Description of a Wave
Example:
A wave is represented by the expression: y= 2cm Sin(3 s-1 t – 5 m-1 x)
Find the amplitude of the wave.
Find the frequency.
Find the wavelength
Find the speed
What is the direction of propagation?

16. 16.4 The Mathematical Description of a Wave
We compare with the general expression
Example:
A wave is represented by the expression: y= 2cm Sin(3 s-1 t – 5 m-1 x)
Find the amplitude of the wave.
Find the frequency.
Find the wavelength
Find the speed
What is the direction of propagation?
A=2cm b) c) d)
e) to the right

17. Check your understanding
Mike is holding one end of a Slinky. His hand moves up and down and causes a transverse wave to travel along the Slinky away from him. Is the motion of Mike’s hand a wave?
a) Yes, the motion of Mike’s hand is a wave because it moves up and down in periodic motion.
b) Yes, the motion of Mike’s hand is a wave because Mike is transferring energy to the Slinky.
c) No, the motion of Mike’s hand is not a wave because there is no traveling disturbance.
d) No, the motion of Mike’s hand is not a wave because there is no energy traveling along the Slinky.

18. The drawing shows the vertical position of points along a string versus distance as a wave travels along the string. Six points on the wave are labeled A, B, C, D, E, and F. Between which two points is the length of the segment equal to one wavelength?
a) A to E
b) B to D
c) A to C
d) A to F
e) C to F

19. 16. 2. 3. A longitudinal wave with an amplitude of 0
A longitudinal wave with an amplitude of 0.02 m moves horizontally along a Slinky with a speed of 2 m/s. Which one of the following statements concerning this wave is true?
a) Each particle in the Slinky moves a distance of 2 m each second.
b) Each particle in the Slinky moves a vertical distance of 0.04 m during each period of the wave.
c) Each particle in the Slinky moves a horizontal distance of 0.04 m during each period of the wave.
d) Each particle in the Slinky moves a vertical distance of 0.02 m during each period of the wave.
e) Each particle in the Slinky has a wavelength of 0.04 m.

20. 16. 3. 1. The tension of a guitar string in increased by a factor of 4
The tension of a guitar string in increased by a factor of 4. How does the speed of a wave on the string increase, if at all?
a) The speed of a wave is reduced to one-fourth the value it had before the increase in tension.
b) The speed of a wave is reduced to one-half the value it had before the increase in tension.
c) The speed of a wave remains the same as before the increase in tension.
d) The speed of a wave is increased to two times the value it had before the increase in tension.
e) The speed of a wave is increased to four times the value it had before the increase in tension.

21. 16.5 The Nature of Sound Waves
LONGITUDINAL SOUND WAVES

22. 16.5 The Nature of Sound Waves
The distance between adjacent condensations is equal to the
wavelength of the sound wave.

23. 16.5 The Nature of Sound Waves
Individual air molecules are not carried along with the wave.

24. 16.5 The Nature of Sound Waves
THE FREQUENCY OF A SOUND WAVE
The frequency is the number of cycles
per second.
A sound with a single frequency is called
a pure tone.
The brain interprets the frequency in terms
of the subjective quality called pitch.

25. 16.5 The Nature of Sound Waves
THE PRESSURE AMPLITUDE OF A SOUND WAVE
Loudness is an attribute of
a sound that depends primarily
on the pressure amplitude
of the wave.

26. Sound travels through gases, liquids, and solids at considerably
16.6 The Speed of Sound
Sound travels through gases,
liquids, and solids at considerably
different speeds.

27. Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb
16.6 The Speed of Sound
Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb
There is a rule of thumb for estimating how far away a thunderstorm is.
After you see a flash of lighting, count off the seconds until the thunder
is heard. Divide the number of seconds by five. The result gives the
approximate distance (in miles) to the thunderstorm. Why does this
rule work?

28. Sound waves carry energy that can be used to do work.
16.7 Sound Intensity
Sound waves carry energy that can be used to do work.
The amount of energy transported per second is called the
power of the wave.
The sound intensity is defined as the power that passes perpendicularly
through a surface divided by the area of that surface.

29. Example 6 Sound Intensities
16.7 Sound Intensity
Example 6 Sound Intensities
12x10-5W of sound power passed through the surfaces labeled 1 and 2. The
areas of these surfaces are 4.0m2 and 12m2. Determine the sound intensity
at each surface.

30. 16.7 Sound Intensity

31. For a 1000 Hz tone, the smallest sound intensity that the human ear
can detect is about 1x10-12W/m2. This intensity is called the threshold
of hearing.
On the other extreme, continuous exposure to intensities greater than
1W/m2 can be painful.
If the source emits sound uniformly in all directions, the intensity depends
on the distance from the source in a simple way.

32. 16.7 Sound Intensity
power of sound source
area of sphere

33. The decibel (dB) is a measurement unit used when comparing two sound
16.8 Decibels
The decibel (dB) is a measurement unit used when comparing two sound
intensities.
Because of the way in which the human hearing mechanism responds to
intensity, it is appropriate to use a logarithmic scale called the intensity
level:
Note that log(1)=0, so when the intensity
of the sound is equal to the threshold of
hearing, the intensity level is zero.

34. 16.8 Decibels

35. Example 9 Comparing Sound Intensities
16.8 Decibels
Example 9 Comparing Sound Intensities
Audio system 1 produces a sound intensity level of 90.0 dB, and system
2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.

36. 16.8 Decibels

37. 16.11 The Sensitivity of the Human Ear

38. The Doppler effect is the change in frequency or pitch
of the sound detected by
an observer because the sound
source and the observer have
different velocities with respect
to the medium of sound
propagation.

39. 16.9 The Doppler Effect
MOVING SOURCE

40. 16.9 The Doppler Effect
source moving
toward a stationary
observer
source moving
away from a stationary
observer

41. Example 10 The Sound of a Passing Train
16.9 The Doppler Effect
Example 10 The Sound of a Passing Train
A high-speed train is traveling at a speed of 44.7 m/s when the engineer
sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What
are the frequency and wavelength of the sound, as perceived by a person
standing at the crossing, when the train is (a) approaching and (b) leaving
the crossing?

42. 16.9 The Doppler Effect
approaching
leaving

43. 16.9 The Doppler Effect
MOVING OBSERVER

44. 16.9 The Doppler Effect
Observer moving
towards stationary
source
Observer moving
away from
stationary source

45. Numerator: plus sign applies when observer moves towards the source
16.9 The Doppler Effect
GENERAL CASE
Numerator: plus sign applies
when observer moves towards
the source
Denominator: minus sign applies
when source moves towards
the observer