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One string wave is given by y (x,y) =0...

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.`

Text Solution

Verified by Experts

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)`
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