[Physics] If water is incompressible, how can sound propagate underwater

acousticsfluid dynamicspressurewaves

Since sound travels as longitudinal waves, sound waves should only be able to propagate in a medium through compressions and rarefactions. However, water, as a liquid, is generally treated as an incompressible fluid. Since compression is essential to sound propagation, how do phenomena such as whale calls and underwater speakers work?

Best Answer

Water is compressible (nothing can be completely incompressible). Treating water as incompressible is just a (usually very good) approximation. Therefore, longitudinal waves are possible.

Wikipedia reports the bulk modulus to be about $2.2\ \mathrm{GPa}$. This puts the speed of sound in water at about $$v=\sqrt{\frac{\beta}{\rho}}=\sqrt{\frac{2.2\ \mathrm{GPa}}{1000\ \mathrm{kg/m^3}}}\approx1500\ \mathrm{m/s}$$