# Characteristics of acoustic resonator with a constant gain frequency response

What would be the theoretical characteristics of an acoustic resonator cavity which has a completely flat gain frequency response over 200Hz-3000Hz (Roughly the range of a violin)

In other words, what would a musical instrument look like if it were to have no distortion in the frequency response, only a constant gain.

My thoughts:

• A thin membrane?
• Right angles would probably be bad, but if you just have a circle which gets progressively larger you'd end up with a horn or a bell, which obviously has a resonant frequency
• If the frequency response is absolutely flat, energy is equally spread across all considered frequency, so by definition you can't really say the cavity is a resonate structure (or system). A resonator by definition traps, amplifies energy at specific frequencies. – docscience Dec 14 '18 at 1:25