Question

When a wave passes from one medium into another, which of its properties, speed, wavelength or frequency, stays the same?

Hint:

The wave source, not the medium, fixes how many cycles occur per second.

Answer 1

Step 1. A wave travelling through a medium obeys the relation \(v = f\lambda\), where \(v\) is speed, \(f\) is frequency and \(\lambda\) is wavelength.
Step 2. The frequency of a wave is set by the source producing it, for example the rate at which a vibrating object or an oscillating source creates each wave cycle.
Step 3. When the wave enters a new medium, the source is not being changed, so the rate at which wave crests are produced cannot change either, meaning the frequency stays fixed.
Step 4. The speed of the wave depends on the properties of the medium it is passing through, so speed does change when the medium changes. Since \(v = f\lambda\) and \(f\) stays constant while \(v\) changes, the wavelength \(\lambda\) must also change to balance the equation.
Answer. Frequency remains unchanged when a wave passes from one medium to another, while speed and wavelength both change.