From the harmonic motion of spring mass, naturally, Prof. Shankar leads to the next topic – waves, which is a common phenomena in life and also so vitally important that we cannot live without waves (sound, light etc. are all waves)

First of all, how to describe such a phenomena?

Now the physicists applied differentiation math techniques and deduce the wave equation:

To solve this partial differentiation equation, one of the concrete solutions is as follows. k = 2pie/lumbda

If we fix the x or location, then to study how the function varies according to time as follows and w = 2pie/T

combine together

velocity of the wave v = w/k, same as v = lumbda/Tperiod = lumbda* frequency.

Second part, he went to talk about another kind of wave – Doppler effect.