notes14a

# notes14a - Sound Waves Sound is a longitudinal wave It...

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Sound Waves Sound is a longitudinal wave It requires a medium to convey it, e.g. a gas, liquid, or solid In a gas, the amplitude of the sound wave is air pressure – a series of slightly enhanced (crest) and reduced (trough) pressure (or air density) regions The speed that these pressure variations move (the wave speed) is the speed of sound

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A sound wave is longitudinal since, for example, the air molecules’ positions oscillate in the direction that the wave travels – they oscillate from condensed regions (crest) to underdense regions (trough) Table 14.1 lists the sound speeds for various gases, liquids, and solids The sound speed in solids > liquids > gases Given some physical properties of the medium, it is possible to calculate the sound speed For ideal gases (low density gases for which the gas atoms or molecules do not interact - discussed in Chap. 17 ), the speed of sound is:
v gas = γ k b T m m = mass of a gas atom or molecule (kg) T = temperature of the gas (Kelvin, K) For temperature, we must use the absolute scale of Kelvin: T(K)=T(°C) + 273.15 (Chap. 16) k b = Boltzmann’s constant = 1.38x10 -23 J/K Think of k b as a conversion factor between temperature and energy γ = adiabatic index of a gas, a unitless constant which depends on the gas, usually between 1.3-1.7. It is 1.4 for air (Chap. 18)

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Notice that the speed of sound increases with temperature It is also possible to calculate the speed of sound in liquids and solids. We will not consider those expressions. Just be aware of the trends, e.g. v air =343 m/s, v water =1482 m/s, v steel =5960 m/s Example Problem The wavelength of a sound wave in air is 2.74 m at 20 °C. What is the wavelength of this sound wave in fresh water at 20 °C? (Hint: the frequency is the same). Solution: Given λ air = 2.74 m, f air = f water
m 47.6 m) 74 . 2 ( m/s 343 m/s 5960 m 11.8 m) 74 . 2 ( m/s 343 m/s 1482 v v v v v v v = = = = = = = = = = water water air air water water water water air air water air f f f f T λ λ λ λ λ λ λ λ How about for the sound wave in steel?

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