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

`y=3sin"(pi)/(2)(50t-x)`
Particle velocity, `v_(p)=(dely)/(delt)=3((pi)/(2)xx50)cos"(pi)/(2)(50t-x)`
Maximum particle velocity, `v_(p_(max))=75pim//s`
Wave velocity, `v=(omega)/(k)=(50)/(1)=50m//s`
Then, `(v_(p_(max)))/(v)=(75pi)/(50)=(3)/(2)pi`.