Answer to Question #309416 in Physics for Kimie

Question

A wave travelling along a string is describe by y(x,t) = 0.35sin(2.75t – 72.5x).

Determine

i. The velocity with which the wave moves along the string

(2 marks)

ii. The displacement of a particle located at x = 21.5 cm and t = 15.5 sec.

(3 marks)

Answer 1

The general equation of a wave is given by

$$y(x,t) = A\sin(\omega t – k x)$$

In our case

$$y(x,t) = 0.35\sin(2.75t – 72.5x)$$

i. The velocity with which the wave moves along the string

$$v=\frac{\omega}{k}=\frac{2.75}{72.5}=0.038\:\rm m/s$$

ii. The displacement of a particle located at x = 21.5 cm and t = 15.5 sec

$$y(0.215,15.5) = 0.35\sin(2.75*15.5 – 72.5*0.215)\\ =0.33\:\rm m$$