Question

what is the intensity (in W/m^2) of a harmonic longitudinal wave with a pressure amplitude of 7x10^-3 N/m^2 propagating down a tube filled with helium (p=0.179 kg/m^3, v=972 m/s)?

A. 0.6X10^-9
B. 2.2X10^-8
C. 2.6X10^-8
D. 1.4X10^-7
E. 1.0X10^-7

Answer 1

acoustic impedence=pressure/particle velocity
Then use I = P^2/Z

Answer 2

http://en.wikipedia.org/wiki/Acoustic_impedance#Specific_impedance_of_acoustic_components

Answer 3

Would it be \[\frac{ .179 }{ 972 } = Z\]\[\frac{ (7X10^{-3})^{2} }{ Z }=0.266078\]
So the answer would be C?

Answer 4

yes it's C

Answer 5

1. Acoustic impedance is \(Z=\rho.c\) , not \(\dfrac{\rho}{c}\)
where c is the celerity of the acoustic wave

2. Intensity is the mean value of the instantaneous product of pressure and velocity of particles at a given point \(P(t).v(t)\)
When you multiply two proportial harmonic functions, a \(\cos^2(\omega t)\) will appear whose mean value is \(\dfrac 12\).

So intensity is \(I=\dfrac 12 \dfrac{P_o\,^2}{\rho \, c}\)