Wave Motion> Two identical waves (except for direction...

Two identical waves (except for direction of travel) oscillate through a springs and yield a superposition according to the equation
y’ = (0.50 cm) sin

What are the amplitude and speed of the two waves?

What is the distance between nodes?

What is the transverse speed of a particle of the string at the positon x = 1.5 cm when t =9/8 s?

Joel Henriques , 7 Years ago

Grade 12th pass

1 Answers

Arun

Last Activity: 7 Years ago

Dear student

Yes, you do have to take the derivative of this. This is a partial differential equation because y' = (0.005 cm) sin[(π/3)x] cos[(45π)t] is a function of x and t. We need the speed, so that equation represents displacement along the y direction. Take dy'/dt, treating terms with x as constants.
First I'm going to convert the cm to m.
y' = (0.005) sin[(100π)/3)x] * cos[(45π)t]
Now derive using product rule and chain rule.
dy'/dt = 0.005 * sin[(100π)/3)x] * [-sin((45π)t)] * (45π)
= -0.225π * sin[(100π)/3)x] * sin[(45π)t]
Subbing in x = 0.015m and t = 9/8s gives v = -0.65m/s = -65cm/s.
You can check that this works by subbing the the values of x where there are nodes, and your speed should equal 0.

Regards

Arun (askIITians forum expert)