For the travelling harmonic wave y(x,t) =2.0 cos 2pi [8t-0.0060x + 0.27], where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of, (a) 300 cm, (b) 0.75 m, ( c) lambda/4

For the travelling harmonic wave y(x,t) =2.0 cos 2pi [8t-0.0060x + 0.2

1.	For the travelling harmonic wave y(x,t) =2.0 cos 2pi [8t-0.0060x + 0.27], where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of, (a) 300 cm, (b) 0.75 m, ( c) lambda/4
Answer» SOLUTION :Here, `y=2.0 COS 2pi (8t - 0.0060x + 0.27)` =2.0 cos `[2pi (8t-0.0060x) + 2pi(0.27)]` Standard equation for a TRAVELLING wave is, `y= r cos[(2pi)/lambda(vt -x) + phi]` Here, `phi =(2pi)/lambda x = 2pi XX 0.006 x` `(2pi)/lambda = 0.006` (a) When x=300 cm, `phi = 2pi xx 0.006 xx 75` `=3.6 pi` rad. (b) When `x= 0.75 m = 75 cm`, `phi = 2pi xx 0.006 xx 75` `=0.9 pi` rad (c ) When `x=lambda/4`, `phi =(2pi)/lambda xx lambda/4 = lambda/2` rad