I have an exam soon about waves and the electromagnetic spectrum. While I was studying I came across the rule of "A change in wave speed causes a change in wavelength as the frequency cannot change". I tried to work it out in my head but I just couldn't see how it could be possible. Could someone please explain it because I'm very unsure. Thanks :)
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Speed = Frequency x wavelength (V=fλ)
In the case of moving from one medium to another, the speed of the wave going through the medium changes, much like you swinging a bat in the air vs swinging the bat under water. The medium changed (air to water) so your speed slowed down, the time it takes you to complete the swing changes (short to long). Thus the frequency, if the formula is to remain the correct, stays the same. It is this change that causes refraction of the wave.
Alternative way to think of it (above requires an understanding that frequency is proportional to time but not directly time)
When passing from one media to another the energy content of the waves has to stay the same due to the law of conservation of energy.
we know that E=hf where E=Energy of wave, h=planck's constant, f=frequency of wave.
so h being a constant would not change, and f could not change either.
So, the only characteristic of the wave which can change is the velocity and wavelength, which adjust themselves so as to give the same frequency before and after passing through different media.
In the case of moving from one medium to another, the speed of the wave going through the medium changes, much like you swinging a bat in the air vs swinging the bat under water. The medium changed (air to water) so your speed slowed down, the time it takes you to complete the swing changes (short to long). Thus the frequency, if the formula is to remain the correct, stays the same. It is this change that causes refraction of the wave.
Alternative way to think of it (above requires an understanding that frequency is proportional to time but not directly time)
When passing from one media to another the energy content of the waves has to stay the same due to the law of conservation of energy.
we know that E=hf where E=Energy of wave, h=planck's constant, f=frequency of wave.
so h being a constant would not change, and f could not change either.
So, the only characteristic of the wave which can change is the velocity and wavelength, which adjust themselves so as to give the same frequency before and after passing through different media.