Particle motion - not all animals are pressure sensors
Mammalian ears are pressure sensors, indeed the ears of most animals that spend some time in air are. We sense pressure fluctuations in our environment and our brains translate those to a perception of hearing sound. Our hearing system really is very elegant and interesting (it performs realtime, mechanical Fourier Transforms!), but that isn't really a topic for this blog.
The catch is that to be a good pressure sensor you need to be able to detect pressure. We do this by having lots of compressible air in our middle ear, so that pressure from the outside can make our eardrum vibrate. But everyone who's ever tried to dive knows that having all that compressible air in your head can be a problem!
Many fishes and all invertebrates (as far as I know) do not have any air-filled cavities associated with their ears, so they do not suffer from aural problems when diving. But this lack of air in the ear means that it must be mostly full of water, water that does not like to be compressed. in fact water is over 16,000 times harder to compress than air...
Luckily (for those guys), sound pressure waves travel through fluids by having molecules push each other in an orderly, sequential fashion, see the middle example in the video below.
All the particles oscillate around a fixed point, transmitting the signal/pressure wave by pushing the next particle in line. The two other wave types (left and right in the video) are transverse (shear) waves that only occur in solids, and surface (Rayleigh) waves that occur the surface of solids.
Many of the animals that cannot detect pressure changes very well are adept at picking up certain components of how the particles themselves move in the medium.
This particle component of sound is not understood as well as the pressure component, and with respect to modelling it, we're a little stuck.
Nedelec et al.  provides sources for calculating peak particle motion (displacement/velocity/acceleration) from sound pressure, frequency and range from source, but only away from interacting boundaries and under the assumption that the wave is a plane wave i.e. far from the source. So many caveats...
All the following values are peak values; peak particle displacement, peak particle velocity & peak particle acceleration.
Nevertheless I tried to plot the resulting planes in a space given by frequency (1 Hz - 100 kHz) and a large pressure range (0-220 dB re μPa). As much as I like 3D plots, to my surprise, what i found when only looking at the effect of frequency on particle motion surprised me more (Figure 2).
|Figure 1. Depicting how Particle motion related to frequency and pressure. "Plane wave limit" refers to the lower frequency limit where an assumption of plane waves applies (80 Hz at 10 m depth over sand). The "Far field lower limit" is a simple assumption that over two wavelengths from the source, the field behaves as in far field. Adapted from equations in .|
Looking at the same data, but in 2D, it becomes clear that something interesting is going on.In Figure 2 particle acceleration is constant in the near field (left of red line), but becomes dependent on frequency in the far field (right of red line). For the particle velocity the opposite is true; particle velocity is independent from frequency in the far field - not sure this makes intuitive sense, but otherwise it would be no fun!
Note that in this figure i have included the "Plane wave limit" also. This is the limit (here ~80 Hz) at which we can expect sound waves to propagate approximately as plane waves and we can infer particle motion from pressure and frequency  (here at 10 metres depth, sandy seabed).
|Figure 2. Same as Figure 1, but only looking at the effect of frequency on particle motion.|
Fheew.... ok - so why is this important?
First of all most of the animals that we are concerned about rely on coastal (i.e. shallow) or seabed environments in their life-cycle, and protecting them becomes a lot easier if we have an idea about what they experience. For the above example, we have almost no idea about what the particle motion is doing under 80 Hz if we only measure and/or model pressure waves. Close to the seabed (and in it) we start to see propagation as in the video up top, and that makes modelling hard(er).
The good people from  did lots of measurements of particle velocity in a shipbuilding dock showing that for frequencies below 400 Hz the pressure part of the signal no longer correlate "nicely" with the particle velocity.
|This is directly taken from  and you should really check it out, they explain it very well!|
Thanks for reading!
I hope that I have managed to give you a little bit of insight, and hopefully something to think about.
Graphwork from GNU Octave.