Here is a small mechanical music box.

Music box

The tines of a metal comb are tuned to emit a particular frequency when plucked. The material and structural characteristics of the comb, plucking cylinder, and box also determine the amplitude (volume) of the sound produced.

For a box of a particular size, and using the same mechanism, are there limits to the frequencies that can be produced at the same amplitude (or, if it's more meaningful, some constant "acoustic energy")?

IIRC, the frequency and amplitude are both a function of the comb's elastic modulus. Frequency is also a function of the length of the tine.

Suppose I observe that this music box produces an 80dB tone when its 440Hz tine is plucked. Suppose also that this baseline comb is made out of steel. What constraints and relationships apply to the tones that can be produced from such a music box if we alter the comb's construction, within the confines of the box? And what if we further alter the comb's constitution over the range of known (or possible) materials?

(For example: It might be that a diamond comb of the same construction would produce tones of twice the frequency, but that it is so brittle it could not produce more than 10dB without shattering. Or: Increasing the cross-section of the tines might halve the frequency, but would it also limit their potential amplitude/"acoustic output"?)

  • $\begingroup$ There are some results about the possible frequencies for a similar setup in the second answer here. (The difference is that your setup has 1 fixed end and 1 free end.) $\endgroup$ – knzhou Jul 25 '16 at 2:08