Why doesn't the wave's frequency change as it gets refracted?

Question

I know that frequency means a complete wave produced per second. But when the wave gets refracted, it's wavelength decreases. If the wave's wavelength has decreased doesn't it means that the wave has been produced more which causes the frequency to increase? Please explain in simple words :)

Answer 1

If the frequency were to change at a boundary, there is no way it could remain in phase with itself at the boundary. The wavelength (or wavenumber) changes because the frequency is fixed and the speed is different on either side of the boundary.

In the simple case of light at an vacuum/glass interface, the frequency remains constant:

$$ \omega = ck = ck'/n =\omega'$$

and the phase and group velocities change:

$$ v_{p} \equiv \frac{\omega}k = c,\ \ v'_{p}=c/n$$ $$ v_{g} \equiv \frac{d\omega}{dk} = c,\ \ v'_{g}=c/n$$

Answer 2

As simple as it gets? You also have the velocity of the wave in the equation connecting wavelength and frequency: $$v=\lambda\cdot f$$ When you change medium, velocity of the wave will change alongside the wavelength.

As for why this change occurs such that the frequency remains the same, try to understand the JEB's answer. But in layman's terms: Velocity change keeps up with wavelength change.

Answer 3

The frequency is controlled by the source. For a wave that travels from one medium into another, the wave will either speed up or slow down due to the change in the characteristics of the medium that it is traveling in, and the wavelength of the wave will change, according to the equation $v=f\lambda$. This means that wave velocity changes, and wavelength changes, such that the frequency remains constant.

As a thought experiment, imagine that you are shaking a rope up and down at a frequency of your choice. The rope that you are shaking is tied to a thinner rope 3 meters from your hand, and due to this, the smaller rope transmits the wave at a higher velocity than the rope that you have in your hand. When the waves that you are creating get to the smaller rope, they speed up and the wavelength gets longer, but the smaller rope STILL has to move up and down at the frequency that you are shaking the rope in your hand.