A travelling wave in a stretched string is described by the equation `y = A sin (kx - omegat)` the maximum particle velocity is

Options

A. `A omega`
B. `omega//k`
C. `dx//dk`
D. `x//1`

Answer

A

Explanation

Given that, the displacement of a particle is
`y=A sin (omega t=kx)` ...(i)
The particle velocity, `v_(p)=(dy)/(dt)` ...(ii)
Now, on differentiating Eq. (i) with respect to t,
`(dy)/(dt)= A cos (omega t-kx)xx omega`
`implies (dy)/(dt)= A omega cos (omega t-kx)`
From Eq. (ii), we get
`implies v_(p)= A omega cos (omega t-kx)`
For maximum particle velocity, `cos (omega t-kx)=1`
So, `v_(p)=A omega xx1 implies v_(p)=A omega`