m10-2: waves - ii

Copyright © 2018 John Wiley & Sons, Inc. and primarily advanced by Prof. A. Iskandar.

17-1 Speed of Sound (1 of 3) Link to heading

Learning Objectives

• 17.01 Distinguish between a longitudinal wave and a transverse wave.
• 17.02 Explain wavefronts and rays.
• 17.03 Apply the relationship between the speed of sound through a material, the material’s bulk modulus, and the material’s density.
• 17.04 Apply the relationship between the speed of sound, the distance traveled by a sound wave, and the time required to travel that distance.

17-2 Traveling Sound Waves (1 of 6) Link to heading

Learning Objectives

• 17.05 For any particular time and position, calculate the displacement $s(x, t)$ of an element of air as a sound wave travels through its location.
• 17.06 Given a displacement function $s(x, t)$ for a sound wave, calculate the time between two given displacements.
• 17.07 Apply the relationships between wave speed $v$, angular frequency $\omega$ angular wave number $k$, wavelength $\lambda$ period $T$, and frequency $ƒ$.

17-2 Traveling Sound Waves (2 of 6) Link to heading

• 17.08 Sketch a graph of the displacement $s(x)$ of an element of air as a function of position, and identify the amplitude $s_m$ and wavelength $\lambda$.
• 17.09 For any particular time and position, calculate the pressure variation $\Delta p$ (variation from atmospheric pressure) of an element of air as a sound wave travels through its location.
• 17.10 Sketch a graph of the pressure variation $\Delta p(x)$ of an element as a function of position, and identify the amplitude $\Delta p_m$ and wavelength $\lambda$.

17-2 Traveling Sound Waves (3 of 6) Link to heading

• 17.11 Apply the relationship between pressure-variation amplitude $\Delta p_m$ and displacement amplitude $s_m$.
• 17.12 Given a graph of position $s$ versus time for a sound wave, determine the amplitude $s_m$ and the period $T$.
• 17.13 Given a graph of pressure variation $\Delta p$ versus time for a sound wave, determine the amplitude \Delta p_m$and the period$T$.

17-3 Interference (1 of 6) Link to heading

17.14 If two waves with the same wavelength begin in phase but reach a common point by traveling along different paths, calculate their phase difference $\phi$ at the point by relating the path length difference $\Delta L$ to the wavelength $\lambda$.

• 17.15 Given the phase difference between two sound waves with the same amplitude, wavelength, and travel direction, determine the type of interference between the waves (fully destructive interference, fully constructive interference, or indeterminate interference).
• 17.16 Convert a phase difference between radians, degrees, and number of wavelengths.

17-4 Intensity and Sound Level (1 of 6) Link to heading

• 17.17 Calculate the sound intensity $I$ at a surface as the ratio of the power $P$ to the surface area $A$.
• 17.18 Apply the relationship between the sound intensity $I$ and the displacement amplitude $s_m$ of the sound wave.
• 17.19 Identify an isotropic point source of sound.
• 17.20 For an isotropic point source, apply the relationship involving the emitting power $P_s$, the distance $r$ to a detector, and the sound intensity $I$ at the detector.

17-4 Intensity and Sound Level (2 of 6) Link to heading

17.21 Apply the relationship between the sound level $\beta$, the sound intensity $I$, and the standard reference intensity $I_0$.

• 17.22 Evaluate a logarithm function $(\log)$ and an antilogarithm function $(\log^{-1})$.
• 17.23 Relate the change in a sound level to the change in sound intensity.

17-5 Sources of Musical Sound (1 of 3) Link to heading

Learning Objectives

• 17.24 Using standing wave patterns for string waves, sketch the standing wave patterns for the first several acoustical harmonics of a pipe with only one open end and with two open ends.
• 17.25 For a standing wave of sound, relate the distance between nodes and the wavelength.
• 17.26 Identify which type of pipe has even harmonics.
• 17.27 For any given harmonic and for a pipe with only one open end or with two open ends, apply the relationships between the pipe length $L$, the speed of sound $v$, the wavelength $\lambda$ the harmonic frequency $ƒ$, and the harmonic number $n$.

17-6 Beats (1 of 2) Link to heading

Learning Objectives

• 17.28 Explain how beats are produced.
• 17.29 Add the displacement equations for two sound waves of the same amplitude and slightly different angular frequencies to find the displacement equation of the resultant wave and identify the time-varying amplitude.
• 17.30 Apply the relationship between the beat frequency and the frequencies of two sound waves that have the same amplitude when the frequencies (or, equivalently, the angular frequencies) differ by a small amount.

17-7 The Doppler Effect (1 of 5) Link to heading

• 17.31 Identify that the Doppler effect is the shift in the detected frequency from the frequency emitted by a sound source due to the relative motion between the source and the detector.
• 17.32 Identify that in calculating the Doppler shift in sound, the speeds are measured relative to the medium (such as air or water), which may be moving.

17-7 The Doppler Effect (2 of 5) Link to heading

• 17.33 Calculate the shift in sound frequency for (a) a source moving either directly toward or away from a stationary detector, (b) a detector moving either directly toward or away from a stationary source, and (c) both source and detector moving either directly toward each other or directly away from each other.
• 17.34 Identify that for relative motion between a sound source and a sound detector, motion toward tends to shift the frequency up and motion away tends to shift it down.

17-8 Supersonic Speeds, Shock Waves (1 of 3) Link to heading

Learning Objectives

• 17.35 Sketch the bunching of wavefronts for a sound source traveling at the speed of sound or faster.
• 17.36 Calculate the Mach number for a sound source exceeding the speed of sound.
• 17.37 For a sound source exceeding the speed of sound, apply the relationship between the Mach cone angle, the speed of sound, and the speed of the source.

Summary Link to heading

• Sound Waves
  • Speed of sound waves in a medium having bulk modulus and density $$\tag{17-3} v = \sqrt{\frac{\beta}{\rho}}$$
• Interference
  • If the sound waves were emitted in phase and are traveling in approximately the same direction, $\phi$ is given by $$\tag{17-21} \phi = \frac{\Delta L}{\lambda} 2 \pi.$$
• Sound Intensity
  • The intensity at a distance $r$ from a point source that emits sound waves of power $P_s$ is $$\tag{17-28} I = \frac{P_s}{4\pi r^2}.$$
• Sound Level in Decibel
  • The sound level b in decibels (dB) is defined $$\tag{17-29} \beta = (10 {\rm dB}) \log \frac{I}{I_0}$$ where $I_0$ ($10^{-12} \ {\rm W/m^2}$) is a reference intensity.
• Standing Waves in Pipes
  • A pipe open at both ends $$\tag{17-39} f = \frac{v}{\lambda} = \frac{nv}{2L}, \ \ \ \ n = 1, 2, 3, \dots.$$
  • A pipe closed at one end and open at the other $$\tag{17-41} f = \frac{v}{\lambda} = \frac{nv}{4L}, \ \ \ \ n = 1, 3, 5, \dots.$$
• The Doppler Effect
  • For sound the observed frequency $ƒ’$ is given in terms of the source frequency $ƒ$ by $$\tag{17-47} f’ = f \frac{v \pm v_D}{v \pm v_S}$$
• Sound Intensity
  • The half-angle $\theta$ of the Mach cone is given by $$\tag{17-57} \sin \theta = \frac{v}{v_S}$$

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