Question

The displacement y of a wave travelling in the x - direction is y=10−4sin(600t–2x+π3)m, where, x is in m and t is in s. The speed of the wave motion in m/s is

Answer 1

points)

The displacement y of a wave travelling in the x -direction is given by

y = 10-4sin(600t - 2x + π/3) metre,where x is expressed in metre and t in second. The speed of the wave-motion, in ms-1 is

300

Answer 2

Given that,

The displacement of a wave travelling in the x -direction is given by :

$y=10^{-4}\sin (600t-2x+\dfrac{\pi}{3})$ ......(1)

To find,

The speed of the wave motion.

Solution,

The general equation of a wave is given by :

$y=A\sin (\omega t-kx+\phi)$  .....(2)

The speed of a wave is given by :

$v=\dfrac{\omega}{k}$

On comparing equation (1) and (2) we get :

$\omega=600$

k = 2

so, velocity is :

$v=\dfrac{600}{2}\\\\v=300\ m/s$

So, the speed of the wave motion is 300 m/s.

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