A traverse wave is repersented by the equation
`y=y_(0)sin(2pi)/(lambda)(vt-x)`
For what value of `lambda` the maximumn particle velocity equal to two times the wave velocity

Explanation

Wave velocity, `v=("Coefficient of t")/("Coefficient of x")`
`therefore v=(2piupsilon)/(2pi//lambda)=lambdaupsilon`
Maximum particle velocity, `V=omegaa=2piupsilony_(0) [because a=y_(0)]`
Now, as per question,
`V=4v or 2piupsilony_(0)=lambdaupsilonxx4`
`or lambda=(piy_(0))/(2)`