[hexane360]

Your result is correct but your explanation is all kinds of wrong. First, shorter wavelength waves have higher energy. Second, amplitude doesn't cause the difference here. Even if you needed 1000W of bass to get the same effect as 10W of treble, 50% attenuation of bass would sound the same as 50% attenuation of treble.

The real difference is that waves are attenuated much more by objects larger than their wavelength.

[TheOtherHobbes]

Sound isn't light. If you have source for your suggestion that shorter wavelengths of sound carry more energy, I'd be curious to see it.

And no, the real difference isn't that waves are attenuated much more by objects larger than their wavelengths. A 200m^2 sheet of paper will still attenuate treble and be completely transparent to bass.

The real difference is that bass damping requires a combination of size, raw mass, and permeability.

It's true that a tiny stick of a bass-damping material will do nothing to stop bass, but it's also true that giant bass traps - like the ones used in studios - will stop treble dead, but their effectiveness at bass frequencies depends entirely on size, thickness, and the material they're made of.

A concrete wall has plenty of mass but no permeability, so it's a good reflector at most frequencies. Bass traps use permeable materials like mineral fibre which have no effect in thin slices, but they're made thick enough to provide enough mass to damp the pressure oscillations.

[saltcured]

I believe that, at a fixed amplitude, the power level increases with frequency for acoustic waves just like EM waves. Ultimately, this comes down to the area under the sin wave. The energy density under the curve increases as you cram more cycles into the same time interval.

Fixed amplitude is the important part here. Amplitude is not a perceptual loudness nor a sound pressure measurement. Sound pressure measurements are already a power scale and so two sounds with the same sound pressure carry the same energy per unit time. Perceptual loudness is even more confusing, as it applies a weighted curve to negate the non-uniform response of the human ear. A higher sound pressure level in bass or very high frequency is required to elicit the same perceived loudness as in our mid-frequency hearing.

Sound amplitude means the maximum particle displacement in one cycle, like the maximum throw of a speaker diaphram. It is a distance, much like amplitude of an electric signal is voltage. A woofer or tweeter with the same amplitude would have the same throw! Those objectionable bass noises from downstairs might involve a half inch or inch of displacement of a subwoofer. When is the last time you saw a tweeter with a half inch of throw? I don't think that would be blocked by tissue paper... it might melt your face off instead.