Question

A standing wave is established on a string that is fixed at both ends. If the string is vibrating at its fundamental frequency, how is the length of the string related to the wavelength of the standing wave?

Answer 1

The concept related to solving the problem is called Standing Waves: This property relates to how, through a chain that is fixed at both ends, it has a fundamental frequency that relates the wavelength of a standing wave to the length of rope.

In other words, if we take a wave that travels in a direction on the rope from one direction, it will immediately tend to return but in the opposite direction. When having two waves traveling in the opposite direction, it is necessary to take into account that during the vibration two reflections are generated on each side. This concept sometimes called constructive interference results in a wave reflection of the type,

$\frac {n} {\lambda 2} = L$

Where n is a positive integer,

λ is the wavelength

L is the length of the chain.

In this way it is possible to appreciate that the length of the string is equal to half of a wavelength.