What Determines the Speed of Waves?

[duran9987]

Homework Statement

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 into play if the medium is the only dependent?

Homework Equations

none

The Attempt at a Solution

 

[haruspex]

In many contexts, the properties of the medium determine the speed of waves in it independently of their wavelengths. This is (mostly) true of waves in a stretched string and waves in a 3 dimensional compressible medium. Any deviation from this is known as dispersion. In particular, it does not apply to 2 dimensional waves, such as surface waves on water. See http://en.wikipedia.org/wiki/Dispersion_(water_waves).

Regardless of what determines the speed of a wave, its frequency and wavelength are always related by v = λƒ.