The tesla coils just have to compress the air the similarly to the magnets in an headphone. With only one magnet you can produce any sound. The same can apply to the coil. But dont ask me how to do that though.
You are either bored to explain eee
And cause I don't like people saying that this is not possible (generally speaking) I'll give an idea on how this is done.
In a AM transmitter we have a carrier wave. The carrier wave is always transmitter in one fixed frequency. This means we have a distortion in a certain frequency, but me can also vary amplitude. For example:
x = A*sin(ωt + θ).
A = Amplitude
ω = radial speed
t = time
θ = starting phase.
Ignore θ (θ = 0) and let's have a look at the rest. The carrier wave frequency in given by: f = ω/2π
Let's say freq is at 200/π Hz then ω = 400 rad/s and we are here:
x = A*sin400t
The graphics are like this:http://upload.wikimedia.org/wikipedia/commons/3/38/Sine_cosine_plot.svg
This is the carrier wave!!!
Now pay attention.
If we vary A which is the Amplitude, we have a second distortion.
In the Tesla Coil occasion we have a simple harmonic distortion in order to have AC current and the spark and a second random distortion which is the sound!!!
This is Amplitude Modulation or AM for more common!!!
Hope that helped!!!