Question

The displacement of a wave travelling in the x-direction is `y = 10^-4 sin [ 600t - 2x + pi/3]`, where x is in metres and t in seconds. The speed of the wave is ______.

Options

• 200 m/s

• 150 m/s

• 600 m/s

• 300 m/s

Answer 1

The displacement of a wave travelling in the x-direction is `y = 10^-4 sin [ 600t - 2x + pi/3]`, where x is in metres and t in seconds. The speed of the wave is 300 m/s.

Explanation:

The displacement of waves,

`y = 10^-4 sin (600t - 2x + pi/3)m`

Compared with the standard equation,

y = asin(ωt - kx + Φ) we get

ω = 600, k = 2

As we know, k = `(2pi)/lambda = (2piν)/(lambdaν) = omega/"v"` [∵ v = vλ]

⇒ v = `omega/k = 600/2 = 300` ms^-1