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=(nx_(0))/(4)`
B. `lamda=2pix_(0)`
C. `lamda=(pix_(0))/(2)`
D. `lamda=4pix_(0)`

Answer

C

Explanation

Particle velocity `=(d)/(dt)(x)`
`=(d)/(dt)[x_(0)sin2pi(nt-(x)/(lamda))]`
`=2pinx_(0)cos2pi(nt-(x)/(lamda))`
Particle velocity will be maximum when
`cos2pi(nt-(x)/(lamda))` is maximum ie. 1.
Wave velocity `=(lamda)/(T)=nlamda`
Now, `2pinx_(0)=4nlamda`
`lamda=(2pinx_(0))/(4n)`
`=(pix_(0))/(2)`