A longitudinal wave is represented by
`x = x_(0) "sin"2pi("nt" - ("x")/(lambda))`
The maximum particle velocity will be four times the wave velocity if

Options

A. `lamda= (pi x_0)/4`
B. `lamda =2 pi x_0`
C. `lamda =(pi x_0)/2`
D. `lamda =4 pi x_0`

Answer

C

Explanation

Particle velocity
`v=d/(dt)[x_0 sin2pi(nt-x/lamda)]=2pi nx_0cos2pi(nt-x/lamda)`
`therefore` Maximum particle velocity `=2 pi nx_0`
Wave velocity =`lamda /T= n lamda`
Given `2 pi nx_0=4n lamda implies lamda= (2 pi nx_0)/(4 n)= (pi x_0)/2`