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A wave equation which given the dispplac...

A wave equation which given the dispplacement along the y-direction is given by ,
`y = 10^(-4)sin (60t +2x)`
where x and y are in matre and t is time in second. This represents a wave

A

travelling with a velocity of `30 m//s` in the negative x-direction.

B

of wavelength `pi m`

C

of frequency `30//pi Hz`

D

of amplitude `10^-4 m` travelling along the negative x-direction.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`y = 10^(-4) sin (60 t + 2 x)`. Comparing the given equation with the stansard wave equation travelling in negative x-direction,
`y = a sin(omega t + kx)`
We get amplitude `a = 10^(-4) m`
Also `omega = 60`
`:. 2 pi f = 60 rArr f = (30)/(pi) Hz`
Also, `k = 2`
`rArr (2 pi)/(lamda) = 2 rArr lamda = pi m`
We know that
`v = f lamda = (30)/(pi) xx pi = 30 m//s`.
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