What is the longest sound wavelength my gym's sound system can support?

[narfarnst]

Sorry it's so wordy, my professor's... well he likes wordy problem's I guess.

Homework Statement

I have very bad acoustics in my gym, where I have a sound system.
To model my gym’s sound system, imagine that the gym is a
cube 4m in length on each side. It’s empty, and the floor, walls,
and ceiling are perfectly flat and reflect sound perfectly (an acoustical
worst‐case scenario!). As a result, its boundary condition is
that any sound wave is always zero at the floor, walls, and ceiling.
Compute the longest sound wavelength that the room can support
and its frequency (recall that the speed of sound is 350m/s). Write
down an expression for all the wavelengths and frequencies that
the room can support.
Now imagine that you’re standing with your head precisely at the
center of the room, and notice that you’re at a “node” for some frequencies
and so won’t be able to hear them. Which frequencies
are those? If you’ve ever been in a theater with poor acoustics,
where your friends beside you could hear fairly well but you
couldn’t, you’re probably familiar with this effect.

Homework Equations

d=vt, v=Lf, (L=lambda) and maybe harmonics.

The Attempt at a Solution

So far, my idea is to basically use V=Lf and plug in the room length to somehow find the frequency and period of the biggest possible wave the room can hold. Then, find it's harmonics. But is this the right approach?

Thanks.

 

[diazona]

Yep, you've got the right idea. Try it, and feel free to post your progress here if you have problems.