One string wave is given by y (x,y) =0.1 sin {pi(5x-2t)} with all the values in SI units. Find (a) amplitude (b) wave length (c ) periodic time, frequency and displacement of this wave at x=3 m and t=2s.

One string wave is given by y (x,y) =0.1 sin {pi(5x-2t)} with all the

1.	One string wave is given by y (x,y) =0.1 sin {pi(5x-2t)} with all the values in SI units. Find (a) amplitude (b) wave length (c ) periodic time, frequency and displacement of this wave at x=3 m and t=2s.
Answer» Solution :Given `y=0.1 sin (5pi x -2pit)` We have `y=a sin (kx - omega t)` COMPARISON gives: (a) AMPLITUDE `a =0.1 m` (b) `k = 5pi (RAD)/(m) implies (2pi)/(lamda) = 5pi implies lamda = 0.4m` (c ) `omega =2pi (rad)/(s) implies (2pi)/(T) = 2pi implies T=1 s` `f = 1/T=1/1 =1 Hz` `y =0.1 sin {(5x xx 3) -(2pi xx 2)}` `=0.1 sin (11pi) =0.1 sin (10 pi+pi)` `THEREFORE y =0.1 sin pi =0""(because sin pi =0)`