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ps07 - Physics 2214 Problem Set#7(Due 11:15 am Thursday 1...

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Page 1 of 2 Physics 2214 Problem Set #7 (Due 11:15 am, Thursday 10/23/07) 1. In a sound wave s ( x , t )—with no dependence on y or z —the instantaneous power per unit cross-sectional area is defined as inst s s I B x t ≡ − and the energy densities (per unit volume) are ( ) 2 1 k 2 / u s t ρ = and ( ) 2 1 p 2 / u B s x = . [Note how similar these expressions are to the power and energy densities in a transverse wave on a string.] (a) Show that, for a traveling sound wave in the ± x direction, I inst ( x , t ) = ± v u ( x , t ), where u ( x , t ) is the total energy density. Interpret this result by considering the energy in a small volume of fluid. (b) The intensity I is defined as the time-average of I inst . A traveling harmonic sound wave has the form ( ) 0 ( , ) cos p x t p kx t ω = where p 0 is the amplitude of the pressure fluctuation. Find the intensity of this wave. Express your answer in terms of p 0 and other constants as needed.

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