in the given progressive wave y = 5 sin (100 pi t -0.4 pi x) where yand x are in metre, t is in second. What is the (a) amplitude (b) wave length (c) frequency (d) wave velocity (e) particle velocity amplitude,

in the given progressive wave y = 5 sin (100 pi t -0.4 pi x) where ya

1.	in the given progressive wave y = 5 sin (100 pi t -0.4 pi x) where yand x are in metre, t is in second. What is the (a) amplitude (b) wave length (c) frequency (d) wave velocity (e) particle velocity amplitude,
Answer» Solution :Comparing give equation, `y = 5 SIN (100 pi t 0.4 pix)` with `y = a sin (omega t - kx + phi)` we get `a= 5m, k = 0.4pi =- (2pi)/(lamda ) implies lamda = 5m` `omega = 100 pi = 2pi f implies f = 50 Hz` `V = (omega )/(k) = (100 pi)/(0.4pi) = 250 (m)/(s)` Maximum velocity of particle performing S.H.M. and taking part in the propagation of wave, `v _(max) = a omega` `= 5 xx 100 pi` `= 500 pi m//s`