Question

A wave is represented by the equation y = 0.20 sin [ 0.4π (x – 60t)], where x and y are in cm and t is in s. The velocity of the wave is...

Answer 1

Answer:

v = 60 m/s

Explanation:

It is given that,

A wave is represented by the equation :

$y=0.2\sin [0.4\pi (x-60)t]$

We need to find the velocity of the wave

The general equation of a wave is given by :

$y=A\sin (kx-\omega t)$ ....(1)

Equation (1) can be written as :

$y=0.2\sin (0.4\pi x-24\pi t)$ ...(2)

If we compare equation (1) and (2) we get :

$k=0.4\pi$

$\omega=24\pi$

The velocity of a wave is given by :

$v=\dfrac{\omega}{k}\\\\v=\dfrac{24\pi}{0.4\pi}\\\\v=60\ m/s$

So, the velocity of the wave is 60 m/s.