Why the higher the frequency the shorter the wavelength?

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This is perhaps best visualized by watching what happens on a lake or swimming pool of water etc. watching what is happening in the surface of water.


More or less the speed of propagation of a wave is constant. Strictly speaking it is non independant of frequency but for many practical purposes it can be assumed constant.


For example we can readily confirm that if we do a disturbance on water, no matter what the disturbance is, the disturbance travels at constant speed.


Now if we gently touch water with our finger or a stick we see a concentric circle travel at the speed of propagation of wave in water. If we do again while the first expanding circle is already traveling we can see another smaller circle starting doing the same.


Clearly the faster we move the water up and down with our finger or stick the more concentric circles we create. And the closer they are to each other.


The distance between consecutive crests is called a wavelength.


So clearly the higher the frequency the shorter the wavelength.


Or in other words the lower the frequency the longer the wavelength.



A great university level book on waves is: Waves - Berkeley Physics Course - vol 3 - Frank S. Crawford Jr.