The relationship between frequency (f), wavelength (λ), and the speed of a traveling wave (v) is described by the equation:
v = f * λ
where:
- v is the speed of the wave,
- f is the frequency of the wave, and
- λ is the wavelength of the wave.
This equation, known as the wave equation, shows that the speed of a wave is equal to the product of its frequency and wavelength. In other words, the speed at which a wave propagates through a medium is determined by the frequency and the distance between consecutive peaks or troughs of the wave (the wavelength).
To illustrate this relationship, let's consider an example: Suppose you have a wave with a frequency of 10 Hz and a wavelength of 2 meters. By using the wave equation, you can determine the speed of the wave:
v = 10 Hz * 2 m = 20 m/s
So, in this example, the wave is traveling at a speed of 20 meters per second.
This equation holds true for various types of waves, including electromagnetic waves (such as light) and mechanical waves (such as sound waves). The relationship between frequency, wavelength, and speed is fundamental in understanding and analyzing wave phenomena.