The equation of the progressive wave is y =a `sin pi (nt -(x)/(5))` the ratio maximum paritcle velocity to wave velocity is

Options

A. `(pi a)/(5)`
B. `(2pi a)/(5)`
C. `(3 pi a)/(5)`
D. `(4pi a)/(5)`

Answer

B

Explanation

`("Maximum particle velocity")/("Wave velocity") = (omega A)/(v) = (2pi n A)/(n lamda)`
`= ((2pi )/(lamda)) A = KA`
where `K = (2pi)/(lamda)`
The equation, `y = a sin 2pi (nt - (x)/(5))` can be written as `y = a sin (2pi n t - (2pi x)/(5)) = a sin (omega t - (2pi x)/(5))`
Comparing with the standard equation,
`y = A sin (omega t - Kx)`, we get
`K = (2pi)/(5) and A = a " " :.` The ratio `KA = (2pi a)/(5)`