Lecture20 - • In the last couple of lectures we discussed...

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Unformatted text preview: • In the last couple of lectures we discussed waves on a string – these are transverse waves, in which the molecules in the string oscillate up and down as the wave moves horizontally • Sound is also a wave – but it’s a longitudinal wave, in which molecules move back and forth along the direction of wave motion: Lecture 20: Sound Waves High pressure Small displacement Low pressure Large displacement High pressure Small displacement • We can describe the sound wave either in terms of the pressure at a given point: or in terms of how much the air molecules have moved from their normal positions: • The pressure and position amplitudes are related by p x , t ( 29 = π ο + ∆π μ αξ σιν κξ - ϖτ ( 29 y x , t ( 29 = Ασιν κξ - ϖτ+ π 2 = Αχοσ κξ - ϖτ ( 29 ∆ p max = BkA Note that here the displacement variable y is in the same direction as x… Speed of Sound • We found earlier that the speed of waves on a string is • The velocity of any mechanical wave has a similar form • What is the “elastic property” of a gas? – It’s the fractional change in volume for a given change in pressure v = Τ μ Elastic property of string Inertial property of string B = - ∆π ∆ς /ς Bulk modulus • Now we need to find an inertial property for a gas – This is the density • So the speed of sound in a gas is: • The same expression also works to find the speed of sound in a liquid • The expression for a solid is similar: v = Β ρ About 330m/s for air at 1atm and 20 o C v = π ∆Λ/ Λ ρ = Ψ ρ Young’s modulus About 6000m/s for iron Intensity • We’ve already discussed the power transmitted by a wave – now we’ll see how much power is transmitted by a sound wave...
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Lecture20 - • In the last couple of lectures we discussed...

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