# Wave speed of a stretched string

A bit confused here as to what wave speed is dependent on. At first I learned that v = λƒ, and a couple of pages later in my textbook I find that v = √(τ/μ). Also, I found that speed is only dependent on the properties of the medium, specifically its elasticity and mass. Where does wavelength and frequency come in to play if the medium is the only dependent?

Nathanael
Homework Helper
The frequency of the wave depends on the source of the wave (how it is being generated). If you consider a wave on a rope, how frequently you wave your arm up and down will determine the frequency of the wave.
The speed of the wave depends on the tension in and density of the rope. So the medium determines the speed of the wave, but there are infinite combinations of frequency and wavelength that will give the correct speed.
For a given rope under a given tension, the wave will travel at a certain speed and the wavelength will depend on the frequency according to $\lambda=\frac{v}{ƒ}$.

duran9987
The medium plays a very big role in wave speed. If the waves travel along a string, the lower the mass and greater the density of the string, the faster waves travel across the string. Waves also travel much more slowly in the air than they do underwater or along a dense string. I'm sure the source of the wave plays a role in its speed as well, but I'm not sure how. This source has some information on it: http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_WavesAlongStrings.xml

duran9987
Orodruin
Staff Emeritus