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Chapter 16

Chapter 16. Sound and Hearing. Modifications by Mike Brotherton. 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

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Chapter 16

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  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 amplitudeis 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 16.11 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 16.14 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 16.17 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 16.18 below shows some harmonics in a closed pipe. • Follow Example 16.11.

  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 16.12.

  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 16.13 using Figure 16.23 below.

  21. Beats • Beats are heard when two tones of slightly different frequency (fa and fb) are sounded together. (See Figure 16.24 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 16.27 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 16.14 using Figure 16.29 below to see how the wavelength of the sound is affected.

  24. The Doppler effect and frequencies • Follow Example 16.15 using Figure 16.30 below to see how the frequency of the sound is affected.

  25. A moving listener • Follow Example 16.16 using Figure 16.31 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 16.17 using Figure 16.32 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 16.18 using Figure 16.33 below.

  28. Shock waves • A “sonic boom” occurs if the source is supersonic. • Figure 16.35 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 16.19 using Figure 16.37 below.

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