# What is the maximum speed of waves in stagnant water?

I want to learn the maximum speed conditions for a wave in a fluid. I think, Which mechanism causes this limited speed? And How? The water is an understandable example for me. By this question, I hope to understand the inhibitory mechanism of the background.

In my opinion, if the waves created by moving object are existing a Doppler Wall in front of the object, the vibrations of substances of the medium may limit the maximum speed objects according to their vibration frequency.

• In fact, maximum speed of a wave in a medium, is limited by the vibration speed of its compound particles. (with mass or massless). I' d like to learn the mechanism behind this. – Burtay Mutlu Oct 22 '18 at 10:33

## 2 Answers

The fastest a normal wave can move in a speed is the speed of sound (in the medium). A disturbance at one point needs to "inform" the next point that it needs to move, and this happens at the speed of sound.

In practice most waves in fluids are far slower, since their frequency and wavelength are determined by gravity, density and other mechanical properties. In deep water a wave moves with velocity $\sqrt{gL/2\pi}$ where $g$ is the surface gravity and $L$ the wavelength. Long wavelength waves such as tsunamis can move at 800 km/h, or 15% of the sound speed in seawater.

Very intense longitudinal waves, shockwaves, are supersonic. Here the molecules are just pushed forward faster than the speed of sound. This leads to discontinuous changes in pressure, temperature and density that tends to dissipate the wave energy quickly, unlike the oscillating transverse water waves we are familiar with.

The fastest waves in water are sound waves, which are longitudinal compression waves. The speed of sound waves in water is about $1500m/s$.

The speed of sound in a fluid, in general, depends on the stiffness (compressibility, elasticity) and density of the fluid: $v=\sqrt \frac K \rho$. The bulk modulus $K$ indicates how much the fluid resists compression.

To the extent that bulk modulus and density are affected by other conditions, the speed of sound in water also depends on temperature, pressure, salinity, etc.