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

Answer

D

Explanation

`A = a, omega = 2pi b, 2pin = 2pi b`
`:. n = b`
`k = 2pi c`
`(2pi)/(lamda) = 2pi c`
`lamda = (1)/(c)`
`y = A sin 2pi (bt - cx)`
`v_(p) = 2v_(W)`
Aomega = 2 n lamda`
`a 2pi xx b = 2b (1)/(c)`
`c = (1)/(pi a)`