Question

Derive the expression for the particle displacement of a plane progressive harmonic wave. Prove that particle velocity is a head of particle displacement in phase by π\2 .​

Answer 1

Answer:

SHM is represented by x=Asinωt

Then, the velocity and acceleration after differentiation will be

v=Aωcosωt

a=−Aω

2

sinωt

Now, we see displacement is in sinωt & velocity is in cosωt

⇒ Phase difference between x & v=π/2 rad

Similarly, we see velocity in cosωt & acceleration in sinωt

⇒ Phase difference between v & a=π/2rad

Thus, we can conclude that the phase difference between x & a=π rad.