Question

A wave is described by y(x,t) = 0.6 sin(8x – 24t), where x is in meters, y is in centimeters and t is in seconds. How long (in s) does it take the wave to travel 3.5 m?

Answer 1

t = 1.47 s

Explanation:

y(x,t) = 0.6 sin (8 x – 24 t )

compare it with

y = A sin (k x - ω t)

now, A = 0.6

k = 8

ω = 24 rad/s

we know ω = 2πf

`f=(24)/(2\pi)`

`k=(2\pi)/(\lambda)\\\lambda = (2\pi )/(8)`

we know that

`v=\lambda f = (2\pi )/(8)* (24)/(2\pi) = 3m/s`

time taken

t = distance/time

= 4.4 / 3

t = 1.47 s