1. Chapter 16
Sound and Hearing
Modifications by
Mike Brotherton

2. Goals for Chapter 16
To describe sound waves in terms of particle displacements or pressure variations
To calculate the speed of sound in different materials
To calculate sound intensity
To find what determines the frequencies of sound from a pipe
To study resonance in musical instruments
To see what happens when sound waves overlap
To investigate the interference of sound waves of slightly different frequencies
To learn why motion affects pitch

3. Introduction
Most people prefer listening to music instead of noise. Ha! But what is the physical difference between the two?
We can think of a sound wave either in terms of the displace-ment of the particles or of the pressure it exerts.
How do humans actually perceive sound?
Why is the frequency of sound from a moving source different from that of a stationary source?

4. Sound waves Sound is simply any longitudinal wave in a medium.
The audible range of frequency for humans is between about 20 Hz and 20,000 Hz.
Ultrasonic sound waves have frequencies above human hearing and infrasonic waves are below.
Figure 16.1 at the right shows sinusoidal longitudinal wave.

5. Different ways to describe a sound wave
Sound can be described by a graph of displace-ment versus position, or by a drawing showing the displacements of individual particles, or by a graph of the pres-sure fluctuation versus position.
The pressure amplitude is pmax = BkA.
B is the bulk modulus from Ch. 11, which we skipped, where B=-p(x,t)/(dv/V)

6. Amplitude of a sound wave
Follow Examples 16.1 and 16.2 using Figure 16.4 below.

7. Perception of sound waves
The harmonic content greatly affects our perception of sound.

8. Speed of sound waves
The speed of sound depends on the characteristics of the medium. Table 16.1 gives some examples.
The speed of sound:

9. The speed of sound in water and air
Follow Example 16.3 for the speed of sound in water, using Figure 16.8 below.
Follow Example 16.4 for the speed of sound in air.

10. Sound intensity
The intensity of a sinusoidal sound wave is proportional to the square of the amplitude, the square of the frequency, and the square of the pressure amplitude.
Study Problem-Solving Strategy 16.1.
Follow Examples 16.5, 16.6, and 16.7.

11. The decibel scale
The sound intensity level  is  = (10 dB) log(I/I0).
Table 16.2 shows examples for some common sounds.

12. Examples using decibels
Follow Example 16.8, which deals with hearing loss due to loud sounds.
Follow Example 16.9, using Figure below, which investigates how sound intensity level depends on distance.

13. Standing sound waves and normal modes
The bottom figure shows displacement nodes and antinodes.
A pressure node is always a displace-ment antinode, and a pressure antinode is always a displacement node, as shown in the figure at the right.

14. The sound of silence
Follow Conceptual Example 16.10, using Figure below, in which a loudspeaker is directed at a wall.

15. Organ pipes
Organ pipes of different sizes produce tones with different frequencies (bottom figure).
The figure at the right shows displacement nodes in two cross-sections of an organ pipe at two instants that are one-half period apart. The blue shading shows pressure variation.

16. Harmonics in an open pipe
An open pipe is open at both ends.
For an open pipe n = 2L/n and fn = nv/2L (n = 1, 2, 3, …).
Figure below shows some harmonics in an open pipe.

17. Harmonics in a closed pipe
A closed pipe is open at one end and closed at the other end.
For a closed pipe n = 4L/n and fn = nv/4L (n = 1, 3, 5, …).
Figure below shows some harmonics in a closed pipe.
Follow Example

18. Resonance and sound
In Figure 16.19(a) at the right, the loudspeaker provides the driving force for the air in the pipe. Part (b) shows the resulting resonance curve of the pipe.
Follow Example

19. Interference
The difference in the lengths of the paths traveled by the sound determines whether the sound from two sources interferes constructively or destructively, as shown in the figures below.

20. Loudspeaker interference
Follow Example using Figure below.

21. Beats
Beats are heard when two tones of slightly different frequency (fa and fb) are sounded together. (See Figure below.)
The beat frequency is fbeat = fa – fb.

22. The Doppler effect
The Doppler effect for sound is the shift in frequency when there is motion of the source of sound, the listener, or both.
Use Figure below to follow the derivation of the frequency the listener receives.

23. The Doppler effect and wavelengths
Study Problem-Solving Strategy 16.2.
Follow Example using Figure below to see how the wavelength of the sound is affected.

24. The Doppler effect and frequencies
Follow Example using Figure below to see how the frequency of the sound is affected.

25. A moving listener
Follow Example using Figure below to see how the motion of the listener affects the frequency of the sound.

26. A moving source and a moving listener
Follow Example using Figure below to see how the motion of both the listener and the source affects the frequency of the sound.

27. A double Doppler shift
Follow Example using Figure below.

28. Shock waves A “sonic boom” occurs if the source is supersonic.
Figure below shows how shock waves are generated.
The angle  is given by sin = v/vS, where v/vS is called the Mach number.

29. A supersonic airplane
Follow Example using Figure below.