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College Physics for AP® Courses

# Section 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 $vwvw size 12{v size 8{w}} {}$, its frequency $ff size 12{f} {}$, and its wavelength $λλ size 12{λ} {}$ 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 $TT size 12{T} {}$ by

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

$vwvw size 12{v size 8{w}} {}$ 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

$I=PA,I=PA, size 12{I= { {P} over {A} } } {}$

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 $ΔpΔp$

$I= (Δp) 2 2 ρv w ,I= (Δp) 2 2 ρv w , size 12{I= { { left (Δp right )} over {2 ital "pv" size 8{m}} } rSup {2} } {}$

where $ρρ size 12{p} {}$ is the density of the medium in which the sound wave travels and $vwvw size 12{p} {}$ is the speed of sound in the medium.

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

$βdB=10log10II0,βdB=10log10II0, size 12{β left ("dB" right )="10""log" rSub { size 8{"10"} } left ( { {I} over {I rSub { size 8{0} } } } right )} {}$

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 $fobsfobs size 12{f rSub { size 8{"obs"} } } {}$ is:
$fobs=fsvwvw±vs,fobs=fsvwvw±vs, size 12{f rSub { size 8{"obs"} } =f rSub { size 8{s} } left ( { {v rSub { size 8{w} } } over {v rSub { size 8{w} } +- v rSub { size 8{s} } } } right )} {}$
where $fsfs size 12{f rSub { size 8{s} } } {}$ is the frequency of the source, $vsvs size 12{v rSub { size 8{s} } } {}$ is the speed of the source, and $vwvw size 12{v rSub { size 8{w} } } {}$ 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:
$fobs=fsvw±vobsvw,fobs=fsvw±vobsvw, size 12{f rSub { size 8{"obs"} } =f rSub { size 8{s} } left ( { {v rSub { size 8{w} } +- v rSub { size 8{"obs"} } } over {v rSub { size 8{w} } } } right )} {}$
where $vobsvobs size 12{v rSub { size 8{"obs"} } } {}$ 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:
$f1f1 size 12{f rSub { size 8{1} } } {}$ is the fundamental and $LL size 12{L} {}$ 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
$a = Z 2 − Z 1 2 Z 1 + Z 2 2 . a = Z 2 − Z 1 2 Z 1 + Z 2 2 . size 12{a= { { left (Z rSub { size 8{2} } - Z rSub { size 8{1} } right ) rSup { size 8{2} } } over { left (Z rSub { size 8{1} } +Z rSub { size 8{2} } right ) rSup { size 8{2} } } } } {}$
• The intensity reflection coefficient is a unitless quantity.
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