College Physics 2e

Section Summary

College Physics 2eSection Summary

17.1Sound

• 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.

17.2Speed of Sound, Frequency, and Wavelength

The relationship of the speed of sound $vwvw$, its frequency $ff$, and its wavelength $λλ$ is given by

$vw=fλ,vw=fλ,$

which is the same relationship given for all waves.

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

$vw=331m/sT273K.vw=331m/sT273K.$

$vwvw$ is the same for all frequencies and wavelengths.

17.3Sound Intensity and Sound Level

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

$I=PA,I=PA,$

where $PP$ is the power crossing area $AA$. The SI unit for $II$ is watts per meter squared. The intensity of a sound wave is also related to the pressure amplitude $ΔpΔp$

$I= (Δp) 2 2 ρv w ,I= (Δp) 2 2 ρv w ,$

where $ρρ$ is the density of the medium in which the sound wave travels and $vwvw$ is the speed of sound in the medium.

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

$βdB=10log10II0,βdB=10log10II0,$

where $I0 = 10 –12 W/ m2 I0 = 10 –12 W/ m2$ is the threshold intensity of hearing.

17.4Doppler 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 $fobsfobs$ is:
$fobs=fsvwvw±vs,fobs=fsvwvw±vs,$
where $fsfs$ is the frequency of the source, $vsvs$ is the speed of the source, and $vwvw$ 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:
$fobs=fsvw±vobsvw,fobs=fsvw±vobsvw,$
where $vobsvobs$ is the speed of the observer.

17.5Sound 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:
$f1f1$ is the fundamental and $LL$ is the length of the tube.
• The resonant frequencies of a tube open at both ends are:

17.6Hearing

• 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.

17.7Ultrasound

• The acoustic impedance is defined as:
$Z=ρv,Z=ρv,$
$ρρ$ is the density of a medium through which the sound travels and $vv$ is the speed of sound through that medium.
• The intensity reflection coefficient $aa$, 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
$a = Z 2 − Z 1 2 Z 1 + Z 2 2 . a = Z 2 − Z 1 2 Z 1 + Z 2 2 .$
• The intensity reflection coefficient is a unitless quantity.