Question

The displacement of a standing wave on a string is given by y (x,t) = 0.4 sin (0.5x) cos (30t) where x and y are in centimetres. (a) Find the frequency, amplitude and wave speed of the component waves. (b) What is the particle velocity at x=2.4 cm at t=0.8 s?

Answer 1

Here is your answer:

Explanation:

(a) The given equation can be written as the sum of two component waves as

y(x,t)=0.2sin(0.5x−30t)+0.2sin(0.5x+30t)

Hence, the two component waves are

y1(x,t)=0.2sin(0.5x−30t)

travelling in positive x-direction and

Now, ω=30rad/s

and k=0.5cm

Frequency, f=ω/2π=15Hz/π

Amplitude, A=0.2 cm

and wave speed, v=ω/k=30/0.5

=60 cm/s .

b) practice velocity is as follow:

vP(x,t)=∂y/∂t=−12sin(0.5x)sin(30t)

vP(x=2.4cm,t=0.8s)  

=−12sin(1.2)sin(24)

=10.12 cm/s.