The relationship between the velocity of a wave and its wavelength is given by the wave equation:
v = λf
where:
- v is the velocity of the wave,
- λ (lambda) is the wavelength of the wave, and
- f is the frequency of the wave.
The wavelength (λ) of a wave is the distance between two consecutive points that are in phase with each other. It is usually measured as the distance between two identical points on the wave, such as two adjacent crests or two adjacent troughs.
The frequency (f) of a wave represents the number of complete oscillations or cycles of the wave that occur in a given time interval. It is measured in hertz (Hz), which represents cycles per second.
The wave equation states that the velocity of a wave is equal to the product of its wavelength and frequency. In other words, the velocity of a wave is determined by how frequently the wave oscillates (frequency) and the distance covered in one complete cycle (wavelength).
This relationship implies that for a given wave velocity, if the wavelength increases, the frequency decreases, and vice versa. This is because the product of wavelength and frequency must remain constant for a wave with a fixed velocity.
It's worth noting that the wave equation holds true for waves traveling through a homogeneous medium, such as sound waves in air or light waves in a vacuum. In different mediums, the velocity of a wave may depend on other factors like the properties of the medium itself.