# Soundwave intensity due to altitude

1. Jan 30, 2008

### dnoi

1. The problem statement, all variables and given/known data

Consider a flat Earth with an atmosphere that decreases in density as altitude increases such that p = p0*e$$^{-h/H}$$, where p0 is the density of air at zero altitude and H is a constant known as the "scale height." Assume the bulk modulus of air is constant.

a) Show that the intensity of a sound wave of constant wavelength will increase with altitude. (Hint: Assume the velocity changes due to a change in frequency only.)

b) Show that the intensity of a sound wave of constant frequency will decrease with altitude. (Hint: Assume the velocity changes due to a change in wavelength.)

c) Show that the ratio of the derivatives is given by

(dI/dh)$$\left|\lambda=constant$$
$$\overline{(dI/dh)\left|f=constant}$$ = -e$$^{h/H}$$

since i know that the density of air is decreasing with altitude, then that should mean that the density is decreasing as well. and if the density is decreasing, then the intensity of sound waves should decrease with altitude as well, right? since

I = 0.5*p*v*w^2*S^2

so is this just a matter of solving for p in the intensity equation and substituting it in for the equation given in the problem?

Last edited: Jan 30, 2008