Question

Is there any relationship between wave speed and the maximum particle speed for a wave travelling on a string ? If so, what is it ?

Answer 1

Let the wave be $y=Acos(\omega t-kx)$

Thus $v=\frac{\omega }{k}$

and particle speed is given by $\frac{dy}{dt}=A\omega sin(\omega t-kx)$

Maximum particle speed=$(V_p{)}_{max}=A\omega =A(kv)=(kA)v$