Question

A string tied between two post is oscillating at 3Hz. A student determines the standing waves have a length of 4 meters. What is the velocity of the wave?

Answer 1

12 m/s

Step-by-step explanation:

Standing waves are waves that are formed between two fixed points in space, so they cannot propagate, but they are just oscillations about a fixed points. Examples of standing waves are the waves in a string.

The relationship between wavelength, frequency and speed of a wave is given by the wave equation:

`v=f \lambda`

where

v is the speed of the wave

f is its frequency

`\lambda` is its wavelength

For the standing wave in this problem we have:

f = 3 Hz is the frequency of the wave

`\lambda=4 m` is the wavelength

Solving for v, we find the velocity of the wave:

`v=(3)(4)=12 m/s`