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

Answer:

t = 1.47 s

Step-by-step 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

$f=\dfrac{24}{2\pi}$

$k=\dfrac{2\pi}{\lambda}\\\lambda = \dfrac{2\pi }{8}$

we know that

$v=\lambda f = \dfrac{2\pi }{8}\times \dfrac{24}{2\pi} = 3m/s$

time taken

t = distance/time

 = 4.4 / 3

t = 1.47 s