# What does wave refraction cause?

If we look at the wave equation we can get an algebraic understanding of it: $v = f \times \lambda$ where $\lambda$ is the wavelength. Clearly if v alters, either f or $\lambda$ must change. As the frequency is determined by the source of the waves, it remains constant. Due to conservation of momentum the direction alters (provided the waves are not at ${90}^{\circ}$)
Another way of understanding this is to consider the crests as being lines of soldiers - an analogy I’ve use during many times. The soldiers are marching at an angle (say ${45}^{\circ}$) from the concrete parade ground onto,the grass lawn. As they move onto the lawn each soldier slows down, this means the distance between those slower soldiers is reduced.