PHYS 422 Lecture 22 Continuous Systems and Fourier Analysis II

# PHYS 422 Lecture 22 Continuous Systems and Fourier Analysis II

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t i t d Continuous Systems and ourier Analysis Fourier Analysis II

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Longitudinal Waves ave in which the oscillator motion is in the direction of wave in which the oscillator motion is in the direction of the wave propagation propagate as sound waves in all phases of matter first, let’s consider sound waves in a gaseous medium a fixed mass of gas at pressure P 0 that m A P 0 occupies a volume V 0 and has density ρ 0 (equilibrium state) nder the influence of the sound waves l under the influence of the sound waves 0 P Pp VV v ⇒+ lets define the maximum pressure of the 0 0 d ρ ρρ sound wave as p m and p is an alternating component superimposed on P 0
Longitudinal Waves e fractional change in volume is v the fractional change in volume is the fractional change in density is m A P 0 0 V δ = d s ρ = δ and s are ~ 10 -3 for ordinary sound waves and a value of p ~ 10 -10 atm gives l 0 p m g audible sound waves at 1000 Hz small order effects e mass of the gas is equal to the mass of the gas is equal to ( )( ) 00 11 VV V s ρρ = =+ + 1 s s ⇒+ + = ± the elastic properties of the gas are given in terms of the bulk modulus (chap. 3)

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Longitudinal Waves e bulk modulus is the bulk modulus is m A P 0 dP dP BV dV dV =− l V let’s assume a constant value of the adiabatic bulk modulus
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PHYS 422 Lecture 22 Continuous Systems and Fourier Analysis II

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