The equation of a progressive wave is given by `y = 5 cos (100 t - 5x)` where y is in microns, x in metre and t is in second. What is the ratio of the maximum particle velocity to the velocity of wave propagation?

Options

A. `50 xx 10^(-5)`
B. `2.5 xx 10^(-5)`
C. `2.5 xx 10^(-4)`
D. `2.5 xx 10^(-7)`

Answer

B

Explanation

`("Maximum particle velocity")/("Velocity of wave propagation") = (omega A)/(V) = KA`
`( :. (omega)/(V) = (2pi n)/(n lamda) = (2pi)/(lamda) = K)`
`y = 5 cos (100 pi - 5x)`
Compare with `y = A cos (omega t - Kx)` we get, `K = 5`
`:.` Ratio `= KA = 5 xx 5 xx 10^(-6) = 2.5 xx 10^(-5)`
(y is in micron) and `A = 5 xx 10^(-6)`