17.1 Sound

• Sound is a disturbance of matter that is transmitted from its source outward.
• Sound is one type of wave.
• Hearing is the perception of sound.

17.2 Speed of Sound, Frequency, and Wavelength

The relationship of the speed of sound $v_{\mathrm{w}}$ its frequency $f,$ and its wavelength $\lambda$ is given by

which is the same relationship given for all waves.

In air, the speed of sound is related to air temperature $T$ by

$v_{\text{w}}$ is the same for all frequencies and wavelengths.

17.3 Sound Intensity and Sound Level

• Intensity is the same for a sound wave as was defined for all waves; it is

  $$I=\frac{P}{A},$$

  where $P$ is the power crossing area $A$. The SI unit for $I$ is watts per meter squared. The intensity of a sound wave is also related to the pressure amplitude $\mathrm{\Delta }p$

  $$I=\frac{{\left(\mathrm{\Delta }p\right)}^2}{2{\text{ρv}}_{\mathrm{w}}},$$

  where $\rho$ is the density of the medium in which the sound wave travels and $v_{\mathrm{w}}$ is the speed of sound in the medium.

• Sound intensity level in units of decibels (dB) is

  $$\beta \left(\text{dB}\right)=\text{10}{\text{log}}_{\text{10}}\left(\frac{I}{I_0}\right),$$

  where $I_0={10}^{\mathrm{–12}}\mathrm{W/}{\text{m}}^2$ is the threshold intensity of hearing.

17.4 Doppler Effect and Sonic Booms

• The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer.
• The actual change in frequency is called the Doppler shift.
• A sonic boom is constructive interference of sound created by an object moving faster than sound.
• A sonic boom is a type of bow wake created when any wave source moves faster than the wave propagation speed.
• For a stationary observer and a moving source, the observed frequency $f_{\text{obs}}$ is
  $$f_{\text{obs}}=f_{\mathrm{s}}\left(\frac{v_{\mathrm{w}}}{v_{\mathrm{w}}\pm v_{\mathrm{s}}}\right),$$
  where $f_{\mathrm{s}}$ is the frequency of the source, $v_{\mathrm{s}}$ is the speed of the source, and $v_{\mathrm{w}}$ is the speed of sound. The minus sign is used for motion toward the observer and the plus sign for motion away.
• For a stationary source and moving observer, the observed frequency is
  $$f_{\text{obs}}=f_{\mathrm{s}}\left(\frac{v_{\mathrm{w}}\pm v_{\text{obs}}}{v_{\mathrm{w}}}\right),$$
  where $v_{\text{obs}}$ is the speed of the observer.

17.5 Sound Interference and Resonance: Standing Waves in Air Columns

• Sound interference and resonance have the same properties as defined for all waves.
• In air columns, the lowest-frequency resonance is called the fundamental, whereas all higher resonant frequencies are called overtones. Collectively, they are called harmonics.
• The resonant frequencies of a tube closed at one end are
  $$f_n=n\frac{v_{\mathrm{w}}}{4L}\text{, }n=\mathrm{1,\; 3,\; 5}\text{.}\text{.}\text{.}$$
  where $f_1$ is the fundamental and $L$ is the length of the tube.
• The resonant frequencies of a tube open at both ends are
  $$f_n=n\frac{v_{\mathrm{w}}}{2L}\text{, }n=\mathrm{1,\; 2,\; 3}\text{.}\text{.}\text{.}$$

17.6 Hearing

• The range of audible frequencies is 20 to 20,000 Hz.
• Those sounds above 20,000 Hz are ultrasound, whereas those below 20 Hz are infrasound.
• The perception of frequency is pitch.
• The perception of intensity is loudness.
• Loudness has units of phons.

17.7 Ultrasound

• The acoustic impedance is defined as
  $$Z=\mathrm{\rho v},$$
  where $\rho$ is the density of a medium through which the sound travels and $v$ is the speed of sound through that medium.
• The intensity reflection coefficient $a,$ a measure of the ratio of the intensity of the wave reflected off a boundary between two media relative to the intensity of the incident wave, is given by
  $$a=\frac{{\left(Z_2-Z_1\right)}^2}{{\left(Z_1+Z_2\right)}^2}.$$
• The intensity reflection coefficient is a unitless quantity.