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Does anyone know of good equipment to measure particle motion in the water, and transferred sound vibrations/pressure through sand underwater (from playbacks)? I have read that some people recommend specific velocity sensors (I assume very expensive) while others recommend accelerometers (not sure what types, but maybe less expensive?). I was hoping someone may have experience taking these measurements and good advice especially about cheaper but reliable solutions. Any advice would be greatly appreciated.

Edit: For depth, not very deep maybe 1-2 meters at most (in a tank) for the water particle motion sensor. For detecting in the sand, it will be about 1-2 m deep and the sand will be only 15-30 cm deep on top of a concrete bottom. The in-water frequency range would be somewhere between 100 Hz - 40 kHz, while the in-sand frequencies would be lower frequencies (e.g., below 1 kHz, likely focusing around 20 - 500 Hz).

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    $\begingroup$ please be more specific: water depth? measurement in water or in sand? frequencies of interest? possible solution will depend $\endgroup$
    – WMXZ
    Jan 21, 2023 at 10:51

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In cases where the sound pressure varies in phase with the velocity of the medium (water/sand) the sound pressure is proportional to the particle velocity (far field condition). See this question discussion and for the formula to estimate particle velocity from sound pressure.

Measuring directly the particle velocity in water is much more difficult than in air, for which some instruments seem to be commercially available (see external links in this wikipedia artcle) that are measure the particle motion via the cooling effect of air motion.

The alternative method to transduce motion directly to electricity uses magnets and is implemented in geophones which are the basic components of ocean bottom seismometers (OBS) used by major research institution for seismic research and placed on the sea bottom. Geophones are however limited to low frequencies (couple of tens of Hz). OBS were found useful to also record sound of low frequency baleen whales.

Most commercially available acoustic vector sensors (AVS) use accelerometers to measure the particle acceleration and particle velocity is obtained by integration. Their frequency response is wider than the one of geophones but still are limited to a couple of kHz.

As particle acceleration is proportional to the sound pressure gradient, accelerometers can be replaced by pairs of closely spaced hydrophones. The bandwidth for this type of particle velocity estimation is limited by the hydrophone spacing, the closer the hydrophone, the wider the bandwidth.

However, in contrast to accelerometers, hydrophones are still useful for higher frequencies forming a sparse hydrophone array.

Measuring directly the particle displacement (e.g. Laser vibration sensor) is not practical in water.

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