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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 = rho_{0}e^{-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}= -e^{h/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.

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# Homework Help: Sound intensity on a flat earth

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