Deeper tones have a longer wavelength. If the resonator is too small compared to the wavelength, it can't transmit the sound efficiently. I guess it has something to do with the sound wave wrapping into itself and causing distortions or something like that.

Deep tones sound better on a concert grand piano than on a small upright where they tend to be somewhat blurry.

Compare with big subwoofers for low-frequency sound reproduction.

Caveat emptor: I'm not really in the business, this is just off the top of my head. :)

Here's some material on how pianos work:

http://www.speech.kth.se/music/5_lectures/contents.html