Question

A transverse wave is represented by the equation
`y=y_0sin.(2pi)/(lamda)(vt-x)`
For what value of `lamda`, the maximum particle velocity equal to two times the wave velocity?
A. `lamda=2piy_(0)`
B. `lamda=piy_(0)//3`
C. `lamda=piy_(0)//2`
D. `lamda=piy_(0)`

Answer 1

Correct Answer - D
On comparing the given equation with standard equation `y=asin.(2pi)/(lamda)(vt-x)`. It is crear that wave speed `(v)_(wave)=v` and maximum particle velocity `(v_(max))_("particle")=aomega=y_0xx` co-efficient of `t=y_0xx(2piv)/(lamda)`
`(v_(max))_("particle")=2(omega)_(wave)implies(axx2piv)/(lamda)`
`=2vimplieslamda=piy_0`