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College Physics for AP® Courses

Section Summary

College Physics for AP® CoursesSection Summary

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 vwvw size 12{v size 8{w}} {}, its frequency ff size 12{f} {}, and its wavelength λλ size 12{λ} {} is given by


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


vwvw size 12{v size 8{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=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.

17.4 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 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.

17.5 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:
    fn=nvw4L n=1, 3, 5...,fn=nvw4L n=1, 3, 5..., size 12{n=1,3,5 "." "." "." } {}
    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:
    fn=nvw2L n=1, 2, 3...fn=nvw2L n=1, 2, 3... size 12{n=1,3,5 "." "." "." } {}

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:
    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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