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in the given progressive wave y = 5 si...

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

Text Solution

Verified by Experts

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`
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