What is the relationship between the frequency and wavelength of a wave?
The relationship between the frequency and wavelength of a wave is described by the wave equation:
Speed = Frequency x Wavelength
This equation states that the speed of a wave is equal to the product of its frequency and wavelength. In simple terms, frequency refers to the number of complete wave cycles that pass a given point in one second, while wavelength is the distance between two corresponding points on adjacent wave cycles.
As an example, if the frequency of a wave is high, it means that the number of wave cycles passing a point per second is greater, hence resulting in a shorter wavelength. Conversely, if the frequency is low, the wavelength will be longer. Therefore, there is an inverse relationship between frequency and wavelength, where an increase in frequency leads to a decrease in wavelength, and vice versa.
The relationship between the frequency and wavelength of a wave is described by a fundamental property of waves called the wave speed. The wave speed is given by the product of the wavelength and the frequency of the wave.
To understand this relationship, it is important to know the definitions of frequency and wavelength.
Frequency (f) is the number of complete cycles of a wave that pass a certain point in a given unit of time. It is commonly measured in Hertz (Hz), which represents one cycle per second.
Wavelength (λ) is the distance between two consecutive points in a wave that are in the same phase, or the distance between two similar points of a wave. It is usually measured in meters (m) or any other unit of length.
Now, the relationship between the frequency and wavelength can be expressed as:
Wave Speed (v) = Frequency (f) × Wavelength (λ)
Mathematically, we can rearrange this equation to solve for either the frequency or the wavelength:
f = v / λ
or
λ = v / f
This means that if the frequency of a wave increases, while the wave speed remains constant, the wavelength will decrease. Conversely, if the frequency decreases, the wavelength will increase, again assuming the wave speed remains unchanged.
Understanding this relationship allows us to calculate the frequency or the wavelength of a wave, given the wave speed, as well as vice versa.