Waves on strings

As an example of a mechanical wave we will first examine waves on strings. You know that if you grab one end of a string or rope, and keeping it taught, flick your wrist that you can send a pulse down the length of the string or rope. The speed at which this pulse pulse propagates is given by

where

• T -- is the TENSION of the string in newtons (N)
• -- is the mass DENSITY of the string per unit length in kilograms per meter (kg/m)

These two concepts: TENSION and DENSITY are both needed to support waves on a string. The symbol c is fairly standard for the speed of waves in acoustics.

You also know that a wave on a string is a TRANSVERSE WAVE, that is, a wave where the wave travels in one direction (along the string) but the string is actually displaced perpendicular to the propagation direction. Example: for a string aligned along the x axis, the string propagates in the x direction, but the displacements are perpendicular to the x axis.