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

Options

A. `2pi`
B. `(3)/(2)pi`
C. `3pi`
D. `(2)/(3)pi`

Answer

B

Explanation

The given equation is
`y=rsin((2pit)/(T)-(2pix)/(lambda))`
`(2pi)/(T)=25pi` or `T=(2)/(25)s`
and `(2pi)/(lambda)=(pi)/(2) ` or `lambda=4m`
Wave velocity, `upsilon=(lambda)/(T)=(4)/(2//25)=50m//s`
Particle velocity, `(dy)/(dt)==3cos(25pit-(pix)/(2))xx25pi`
Max. particle velocity `=((dy)/(dt))_(max)=75pi`
Now, `((dy//dt)_(max))/(upsilon)=(75pi)/(50)=(3)/(2)pi`