Question

A stationary wave is formed by a string between two rigid ends. A particle in the string follows motion $y=\left(5cm\right)sin\left(15x\right)cos\left(120t\right)$. Find the speed of wave moving along the string and the particle velocity.

Answer 1

Equation of the wave : $y=5sin\left(15x\right)cos\left(120t\right)$

compare with standard equation, $y=Asin\left(kx\right)cos\left(wt\right)$ of a standing wave,

we get A=5, w=120 and k=15.

so, velocity of wave is = $\frac{w}{k}=\frac{120}{15}=8cm/s$

and velocity of particle = $Aw=5\times 120=600cm/s.$