Air temperature and diffraction


i’m stuck on a problem that seems not to provide enough information to solve it, but i’m probably missing something…

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

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 has a value of 12 degrees. What is
the diffraction angle for the same sound on a summer day when the temperature is
311 K?

2. Relevant equations

3. The attempt at a solution

I thought that if I could figure out the speed of sound at 311k that might help me find the wavelength and therefore the ratio of wavelength to slit width, but it doesn’t seem to.

[itex]\frac{C_{273k}}{C_{311k}} = \sqrt{\frac{T_{273k}}{T_{311k}}}[/itex]

[itex]C_{311k} = \frac{C_{273k}}{\sqrt{\frac{T_{273k}}{T_{311k}}}}[/itex]

The question doesn’t provide the answer, but I have in my notes that the speed of sound at 273k is 331m/s, so I use this figure to give me the speed of sound at 311k

[itex]C_{311k} = 353.3 ms^{-1}[/itex]

But I can’t seem to do anything useful with this…

I would like to know if I have started down the right path, and if I have, how do I move forward? Alternatively, is there a way to solve this problem using only the data given in the question?



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