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The equation of a simple harmonic motion...

The equation of a simple harmonic motion is given by `y = 3 sin.(pi)/(2) (50 t-x)`, where x and y are in metres and t is in seconds, the ratio of maximum particle velocity to the wave velocity is

A

25 m/s

B

30 m/s

C

50 m/s

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given wave equation is
`y = 3 sin .(pi)/(2)(50 t - x)`
`implies " "y = 3 sin (25 pi t - (pi)/(2)x) " "...(i)`
Comparing with standard equation
`y = a sin (omegat - kx) " "...(ii)`
`omega=25pi, k = pi//2`
Wave velocity,
`v = (omega)/(k)=(25pi)/(pi//2)=50m//s`
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