, and . There is an implicit assumption that (adiabatic, no heat transfer).

Time to equilibriate = . which means so . This means a high enough frequency to be nonadiabatic is .

I can hear from about 100 Hz-16000Hz.

human range is about .

For a piano,

• A1=27.5 Hz,
• middleC 262Hz
• A
• = =

A sound wave causes a change in volume of a bunch of particles by , also

the fluctutation velocity is , so .

.

the quantity, is the acoustic impedance.

source psfile jl@crush.caltech.edu index stress_concentration sound_wave_energy sound_radiation Reynolds_number viscosity