When a wave travels in a medium, the particle displacement is given by the equation
`y=asin 2pi(bt-cx), ` where `a,b` and `c` are constants. The maximum particle velocity will be twice the wave velocity. If

Options

A. `c = (1)/(pi a)`
B. `c = pi a`
C. `b = ac`
D. `b = (1)/(ac)`

Answer

A

Explanation

`y = a sin 2pi (bt - cx)`
Comparing with a `sin 2pi (nt - (x)/(lamda))`
we get `n = b and lamda = (1)/(c)`
`:.` Velocity of the wave `v = n lamda = (b)/(c)`….(1)
Maximum particle velocity
`a omega = a.2pi n = a .2pi b = 2pi ab`...(2)
If `2pi ab= 2 ((b)/(c)), " then " pi a = (1)/(c) or c = (1)/(pi a)`....(3)