Question

Two sinusoidal waves traveling in opposite directions interfere to produce a standing wave with the wave function y = (2.00) sin(0.500x) cos(300t) where x and y are in meters and t is in seconds. (a) Determine the wavelength of the interfering waves. m (b) What is the frequency of the interfering wave? Hz (c) Find the speed of the interfering waves.

Answer 1

Part a)

`\lambda = 4\pi`

Part b)

`f = 47.7 Hz`

Part c)

`v = 600 m/s`

Step-by-step explanation:

Part a)

As we know that angular wave number is given as

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

`k = 0.500`

`0.500 = (2\pi)/(\lambda)`

`\lambda = (2\pi)/(0.500)`

`\lambda = 4\pi`

Part b)

As we know that angular frequency is given as

`\omega = 300 rad/s`

`\omega = 2\pi f`

`300 = 2\pi f`

`f = (300)/(2\pi)`

`f = 47.7 Hz`

Part c)

Speed of the wave is given as

`v = \lambda * frequency`

so we have

`v = 4\pi * 47.7`

`v = 600 m/s`