What determines the frequency of standing waves aside from their length?

The frequency of standing waves is determined by various factors related to the physical properties of the medium and the wave itself. The wave equation, which describes the relationship between the speed of a wave, its frequency, and its wavelength, plays a crucial role in understanding this phenomenon.

Standing waves are formed by the interference of two waves traveling in opposite directions. The fundamental frequency of a standing wave can be derived from the wave equation:

[ v = f \cdot \lambda ]

where ( v ) is the wave speed, ( f ) is the frequency, and ( \lambda ) is the wavelength. While the length of the medium (for example, a string or air column) determines the wavelengths of the standing waves that can exist, the equation shows that frequency is directly related to wave speed and inversely related to wavelength.

The speed of a wave in a given medium can vary based on factors such as tension in a string or the properties of the air, and this speed is crucial for determining frequency. For example, in a solid medium like a guitar string, changing the tension alters the wave speed, which in turn changes the frequency for a given wavelength.

Other factors like the temperature of the medium or the mass of the