Are sounds louder under water?

[BioMedPhD]

Given equal power at the sound source - is the amplitude (in pascals) of sound pressure waves greater in water than in air? - What is the mathematical or physical bases of any difference?

 

[Vanadium 50]

What have you found so far on your one? There is an equation for it.

 

[olivermsun]

Two things to investigate with respect to physical differences between water and air:
1) incompressibility
2) density

 

[sophiecentaur]

Amongst a large number of Google hits, I found this one. The 'loudness' of a sound relates to our perception of it, as well as the actual Power Flux. The relevant quantity here is Acoustic Impedance, which is the ratio of acoustic pressure to acoustic flow. Our hearing system has to Match the energy in Air, which is a very low impedance to the conditions in our Cochlea which, being immersed in a liquid, is a high impedance. The Ossicles do not, as people say "amplify the sound" (they are not amplifiers). They are a set of tiny levers which act as Transformers (matching transformers like you get in sound and RF equipment). They transform the large movement of the ear drum at low pressure in the air to a smaller movement with greater pressure in the inner ear. So we would not perceive a high power sound in water as being as 'loud' as the (same power) sound in air because out system just reduces the amplitude of the vibrations transmitted. Aquatic animals do not need to do this transformation and their hearing under water will be much better.

 

[nasu]

The relationship between intensity and pressure amplitude is $I= \frac{p^2}{2 \rho_0 c}$.
Here I is the intensity in $W/m^2$ , $\rho_0$ is the density of the medium and c is the speed of sound in the medium. The product $Z=\rho_0 c$ is the impedance of the medium.
So for a medium with larger impedance you need larger pressure in order to get the same intensity.
The impedance of water is about 1.5 x 10^6 Rayl and for air just about 450 Rayl. (Rayl is the unit for acoustic impedance in SI, just the name of the combination of units you get when multiply density by speed). So the pressure of sound waves is much larger in water than in air, for the same physical intensity.
But this does not necessarily mean that the sound will be perceived as "louder". It depends how the sound couples to your ear membrane. This was already treated by the above post, by @sophiecentaur.