# Diffraction from a loud speaker

## Homework Statement

Sound exits a diffraction horn loudspeaker through a rectangular opening like a small doorway. Such a loudspeaker is mounted outside on a pole. In winter, when the temperature is 273 K, the diffraction angle θ has a value of 11°. What is the diffraction angle for the same sound on a summer day when the temperature is 307 K?

## Homework Equations

v=sqrt($\gamma$kT/m)
v=$\lambda$f
sin$\theta$=$\lambda$/D

## The Attempt at a Solution

I can't seem to relate these equations. I know that $\gamma$k/m is constant for both T and I also know that v increases with temperature but I don't understand how that affects lambda and frequency.

A good way to approach this problem is to consider the ratio $\frac{sin\theta_f}{sin\theta_i}$ where the subscripts refer to the initial and final temperatures.
So I set that ratio equal to the ratio of vf/vi and then canceled out sqrt($\gamma$k/m) because it is constant in both cases therefore the ratio of Sinfθ/Siniθ is equal to sqrt(Tf)/sqrt(Ti) It was correct.