When a water wave passes through from a deep water to shallow water , refraction is said to occur due to it's decrease in wavelength and thus decrease in speed , based on the formula v=fλ. Question is , why should wavelength decrease in the first place?


2 Answers 2


The relation between the angular frequency $\omega=2\pi f$ and wavenumber $k=2\pi /\lambda$ for waves on shallow water is $$ \omega = k \sqrt{gh}, $$ where $g$ is the gravitational acceleration and $h$ the water depth. Since the frequency cannot change, a reduction in depth leads to an increase in $k$ and hence a shorter wavelength. To derive the $\omega(k)$ relation you need to set up and solve the equations of motion for the fluid. I don't know any easy short cut to this. Water waves are not simple things.


The formula $$ v = f \lambda$$

provides a relation between three quantities. That is all. It is not that a decrease of wavelength "in the first place" causes a change in propagation velocity.

The form of such expressions does not say anything about causation. One can rewrite it as

$$\lambda = \frac{v}{f}.$$

The propagation velocity of the waves is a property of the medium. In this case, it depends on the depth of the water.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.