How reliable are "particle-velocity" microphones?

Question

For studies with insects which are sensitive to air particle-velocity, so called "particle-velocity" microphone are used (e.g. here, here, here, here). However, they are not truly particle-velocity detectors as antennal ears are, because they use 2 pressure microphones next to each other (pressure gradient) to estimate particle velocity (e.g. Knowles NR-33158).

Can we trust these estimations? How precise are they? Does it exist true particle-velocity microphones?

Some fishes detect water-particle velocity. Does the fish bioacoustics community use pressure-gradient hydrophones?

Answer 1

IMHO, there exists some confusion about particle velocity in the bioacoustic world, so some more words

There are couple of aspects to it

• physics: sound propagates in form of varying pressure densities, where (water, air) particles move oscillate around an equilibrium. So any sound can be measured by either pressure difference (deviation from equilibrium) or particle velocity (how fast particle move at equilibrium pressure). It is part of the physics that the particle acceleration is proportional to the pressure gradient (an essential contribution to the wave equation).
• Sound intensity: Sound intensity is in general defined as product between pressure and particle velocity. Far away from the source particle velocity equals to sound pressure divided by acoustic impedance, so that sound intensity becomes proportional to sound pressure squared. To estimate directional sound intensity one needs pressure and particle velocity measurements.
• implementation: there are three methods to 'measure sound': pressure sensors (microphones, hydrophones), accelerometers, and velocity sensors (geophones style). accelerometers and velocity sensors are vector sensors, that is they measure the quantity in 1,2,3 dimensions. True velocity sensors are AFAIK only used in geophysics. Most vector sensors are based on accelerometers that get integrated to obtain particle velocities. As particle acceleration is equivalent to pressure gradient (at least for realistic sound pressures), pressure gradient measurements can be used to estimate the sound intensity. The question remains, how good can the pressure gradient be estimated. For oscillating sound, the pressure follows a sinusoid, so the question becomes how good can the tangent of the zero-crossing of a sinusoid be estimated with two spatially separated sensors (how good approximates a secant the tangent).This is equivalent to assessing the Euler method for differentiation. Obviously, the closer they are the better. However, the closer they are the more will noise contaminate the estimate, so one has to find a compromise.

To assess the reliability, one should note that the sound intensity estimate using pressure gradient methods inverts the sign at spatial Nyquist (wavelength = 2*sensor spacing). In how far this can be compensated could be subject to research

A major advantage of gradient based intensity estimators is that at shorter wavelength(higher frequencies) the spatially separated sensor allow time delay of arrival (TDOA) direction finding, so I'm a big fan of compact Volumetric Acoustic Sensors (work in progress)

Answer 2

To answer the last part of that question which is "does the fish bioacoustics community use pressure-gradient hydrophones"-

Yes, often the two hydrophone method is used to estimate particle motion, but that is only appropriate where propagation conditions are suitable for the method. The two hydrophone method requires high quality hydrophones that can make accurate phase measurements, and then a fair bit of expertise to work out what's going on.

There are a few commercially available sensors which directly measure water-borne particle motion (velocity or acceleration). A few research groups have access to these sensors, but not many, and they are definitely not a common piece of kit. An example of such a sensor is: https://geospectrum.ca/commercial-products/directional-sensors/particle-motion/

It has taken a long time for the underwater bioacoustics community to learn/accept that some fish and invertebrates are sensitive to particle motion alone (rather than pressure), which sort of explains the lag in available sensors. Plus, it's sort of tricky to make a particle velocity sensor for water that is accurate.

For more info on the water-borne side, see: Popper, A. N., and Hawkins, A. D. (2018). “The importance of particle motion to fishes and invertebrates,” J. Acoust. Soc. Am., 143, 470–488. doi:10.1121/1.5021594