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. Water waves are partially transverse and partially longitudinal.
16.1 The Nature of Waves
Water waves are partially transverse and partially longitudinal.

6. 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.

7. 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.

8. 16.2 Periodic Waves

9. 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.

10. 16.2 Periodic Waves AM FM

11. Helpful Hints Velocity can also be expressed as
During each cycle of a wave, an individual particle will move through a total distance that equals 4A (A=amplitude).
Think about that… the particle moves up, to equilibrium, down, to equilibrium.
If necessary, use the identity 4A/T or 4Af to solve for velocity.

12. 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

13. Hints!
When a greater pulling force (Tension) is applied to a string, a greater velocity will result.
A wave travels faster on a string whose particles have a small mass (or on a string that has a small mass per unit length.

14. 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.

15. 16.3 The Speed of a Wave on a String
High E
Low E

16. 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?

17. Answer Particle speed differs from wave speed.
Particle speed varies as in simple harmonic motion and depends on amplitude, frequency, and time. In other words particle speed depends on properties of the source creating the wave.
Speed of the wave is determined by the properties of the medium itself.

18. 16.4 The Mathematical Description of a Wave
What is the displacement y at time t of a
particle located at x?

19. Mathematical Description
(2πft – 2πx/λ) represents the phase angle
When using a calculator to solve for sine of phase angle, set to radian!
This expression relates simple harmonic motion of the particles to the wave motion itself.
y is the displacement of the particle from the origin (undisturbed location) at any given time (t) as the wave passes.

20. 16.5 The Nature of Sound Waves
LONGITUDINAL SOUND WAVES

21. 16.5 The Nature of Sound Waves
The distance between adjacent condensations is equal to the
wavelength of the sound wave.

22. 16.5 The Nature of Sound Waves
Individual air molecules are not carried along with the wave.

23. 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.

24. 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.

25. 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.

26. In a gas, it is only when molecules collide that the condensations and
16.6 The Speed of Sound
In a gas, it is only when molecules collide that the condensations and
rerefactions of a sound wave can move from place to place.
Ideal Gas

27. Speed of Sound
Near room temperature, the speed of sound in air is 343m/s.
Speed of sound depends on the properties of the medium.
In a gas, the speed of sound should have the same order of magnitude as the average molecular speed between collisions given as
Check pg !

28. Speed of Sound
γ is the ratio of specific heat capacity (c) at constant pressure to (c) at constant volume.
γ = 5/3 for ideal monotomic gases
γ = 7/5 for ideal diatomic gases
Use Temperature in Kelvin

29. 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?

30. 16.6 The Speed of Sound
LIQUIDS
SOLID BARS

31. 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.

32. This is Getting very INTENSE!
Power is work per unit of time.
Work is change in energy per unit of time.
Remember, energy can be KE, PE, or Q
Q=cmΔT
Spherically uniform radiation
Intensity of a source that radiates sound uniformly in all directions varies as 1/r2

33. 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.

34. 16.7 Sound Intensity

35. 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.

36. 16.7 Sound Intensity
power of sound source
area of sphere

37. Conceptual Example 8 Reflected Sound and Sound Intensity
Suppose the person singing in the shower produces a sound power P.
Sound reflects from the surrounding shower stall. At a distance r in front
of the person, does the equation for the intensity of sound emitted uniformly
in all directions underestimate, overestimate, or give the correct sound
intensity?

38. 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.

39. Intensity vs. Decibel
Decibel is a dimensionless measurement because it is, in fact, a ratio.
Human ear can not perceive small changes in intensity. In fact, a 1dB change is approximately the smallest detectable change in loudness.
The reason we use a logarithmic scale is because of this fact. Remember, logarithmic scale works on powers of 10.
Doubling intensity does NOT double loudness.
A 10dB increase is intensity is perceived to be twice as loud a original intensity.

40. 16.8 Decibels

41. 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.

42. 16.8 Decibels

43. 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.

44. 16.9 The Doppler Effect
MOVING SOURCE

45. Doppler Effect Simplified
When the source is moving toward the observer, the sound waves get squished together and frequency increases.
As source moves away from observed, sound waves get stretched and frequency decreases.

46. Moving Observer
When the observer moves toward a stationary sound, the observer moves in to more waves per second than if the observer were to stand still.
When the observer moves away from a stationary sound, the observer encounters fewer waves per second than if stationary.

47. Main Difference
Source moving: λ of the sound perceived chances from λ to λ’. Due to the changed λ, the observer hears a different frequency.
Observer moving: λ does not change. Moving observer intercepts a different # of wave condensations per second than does a stationary observer. Therefore a different frequency.

48. 16.9 The Doppler Effect
source moving
toward a stationary
observer
source moving
away from a stationary
observer

49. 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?

50. 16.9 The Doppler Effect
approaching
leaving

51. 16.9 The Doppler Effect
MOVING OBSERVER

52. 16.9 The Doppler Effect
Observer moving
towards stationary
source
Observer moving
away from
stationary source

53. 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

54. 16.10 Applications of Sound in Medicine
By scanning ultrasonic waves across the body and detecting the echoes
from various locations, it is possible to obtain an image.

55. 16.10 Applications of Sound in Medicine
Ultrasonic sound waves cause
the tip of the probe to vibrate at
23 kHz and shatter sections of
the tumor that it touches.

56. 16.10 Applications of Sound in Medicine
When the sound is reflected
from the red blood cells, its
frequency is changed in a
kind of Doppler effect because
the cells are moving.

57. 16.11 The Sensitivity of the Human Ear