# Are the speed of sound and water ripples' speed the same?

When a droplet of water hits the surface of a lake it produces ripples that travel outward. My conception is that it travels at the speed of sound in water (since sound are nothing less that perturbations on the medium).

But ripples travel much slower than that. What's happening? Is my conception of propagation of ripples wrong?

Perhaps that discrepancy is related to the difference between group velocity and phase velocity?

The restoring force for waves on the surface of water is gravity, is why such waves are called "gravity waves" (not gravitational waves!). Gravity waves on deep water have $$\omega_{\rm gravity}(k)= \sqrt{{gk}},$$ which is independent of the density of the water.
The restoring force for sound waves in water is the water's elastic properties and $$\omega_{\rm sound}= \sqrt{\frac{\kappa}{\rho}}k$$ where $$\kappa$$ is the bulk modulus and $$\rho$$ is the density. The waves therefore have completely different origins and properties.
• Interesting. What is $k$ in your first equation? – Gert Feb 27 at 22:04
• It is the wavenumber: $k=2\pi/\lambda$. And $\omega$ is the angular frequency $\omega=2\pi f$. – mike stone Feb 27 at 22:35