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

Options

A. 25 m/s
B. 30 m/s
C. 50 m/s
D. None of these

Answer

C

Explanation

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`