They say the frequency of a wave is its fundamental character, thus remain constant throughout its propagation regardless the medium through which it travels. Could anyone explain why frequency of wave is fundamental character but its wavelength isn't?
Answer
The frequency must remain constant to avoid a discontinuity at the boundary.
The easiest way to see this is to consider 2 ropes of different linear densities - e.g. a thin rope and a thick rope - joined in series.
If you shake one end at a frequency f, then (transverse) waves will travel along the joined ropes. The waves travel slower along the thicker rope than the thin rope.
At the junction between the ropes (and to either side of the junction) the frequency must still be f - it wasn't the rope would have to split due to adjacent points having different frequencies.
The same is true for any wave - you can't have a sudden jump in the electric field of an EM wave for example - the electric field can only vary continuously, with no discontinuities.
As a consequence of remaining constant, wavelength and speed change proportionately (e.g. if speed doubles, wavelength doubles).
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