# Why does a microphone membrane only measure pressure and not particle velocity?

Microphones (e.g. condenser microphone) are assumed to have a voltage output proportional to the sound pressure at the diaphragm.

If the operating principle is that the voltage output is proportional to the displacement of the thin foil that is the diaphragm, then why does the particle velocity of the sound wave not affect the displacement of the diaphragm and hence the measurement?

I know that in acoustics the particle velocity and the acoustic pressure do not have a fixed relationship (except for the case of plane waves), and hence in the near-field of a source, a sound intensity measurement must be taken (uses two microphones to estimate particle velocity).

It is obvious that the force from the acoustic pressure at the film will cause a velocity (hence displacement) of the film, but what about the contribution from particle velocity of the fluid transferring momentum to the film?

• Are high pressure and high particle velocity mutually exclusive? – BMS Mar 25 '14 at 18:28
• @BMS: yes (in the fluid). e.g. destructive interference of two waves will reduce the pressure whilst increasing the particle velocity, or in the near-field of a simple point source the pressure and velocity do not have a simple relationship. – xyz Mar 25 '14 at 18:47

Think about the definition of pressure: $$P=\frac{F}{A}$$ Now, let's consider the definition of a force. $$F=\frac{dp}{dt}=m\frac{dv}{dt}$$ Hence, for a given area and particle mass, the pressure is a function of the velocity: $$P=\frac{m}{A}\frac{dv}{dt}$$