The Speed of a Transverse Wave on a String

Below is a discussion of the speed of a transverse wave on a string as well as the formula for average wave speed and the wave speed of a transverse wave on a stretched string. A stretched string may be made to vibrate transversely or longitudinally.

About transverse wave on a string

However most applications in physics involve transverse waves, rather than longitudinal waves. Transverse waves can then set up longitudinal sound waves in the surrounding medium. The end of the string must be fixed. The reflections at these points or nodes create standing waves.

Transverse standing waves on a stretched string

The Speed of a Transverse Wave on a String formula

The general formula of the wave speed is:

Where:

• v = speed of wave (ms^-1)
• f = frequency of wave (Hz)
•  = wavelength of the wave (m)

For mechanical waves:

where:

• v = speed of the saves (longitudinal or transverse) along a stretched string or spring (ms-¹)
• F = force used (tension) to stretch the string (N)
•  = mass per unit length of string or spring (kgm ^-1)