# Sound intensity on a flat earth

1. Feb 15, 2010

### Gogeta007

Sound intensity on a "flat earth"

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

Consider a flat Earth with an atmosphere that descreases in density as altitude increases such that rho = rho0e-h/H where rho nought 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 soundwave of constant wavelenght will increase with altitude (assume velocity changes due to a change in frequency only). b) Show that the intensity of a soundwave of constant frequency will decrease with altitude (Assume velocity changes due to a change in wavelenght only). c) Show that the ratio of the dreivatives is given by:
(dI/dh) lamda constant / (dI/dh) freq. constant = -eh/H

2. Relevant equations

I = .5p v w^2 S^2
p = rho
w = omega

3. The attempt at a solution
I've been breaking my head trying to do this.
The only thing i can think of is to get all the wanted variables into the equation:

I = .5p (lambda/time) (2pi f)^2 S^2

but then how do I go from there?
I have the feeling that I have to do partial dv/dlambda and partial dv/dfreq.
but I dont know how and where to insert them and use them.

ty.