The relationship between frequency, wavelength, and wave speed is expressed by the equation:

where $v$ represents wave speed, $f$ denotes frequency, and $\lambda$ (lambda) symbolizes wavelength.

In the field of physics, particularly in wave mechanics, this relationship is a fundamental concept. The equation $v = f \lambda$ succinctly captures how these three variables interact. Here, wave speed $v$ is the rate at which a wave propagates through a medium, typically measured in meters per second (m/s). Frequency $f$ refers to the number of complete wave cycles that pass a fixed point within a specific time frame, usually quantified in hertz (Hz). Wavelength $\lambda$ is defined as the distance between corresponding points on consecutive waves, such as from crest to crest or from trough to trough, and is measured in meters (m).

The equation $v = f \lambda$ illustrates that the speed of a wave is directly proportional to both its frequency and its wavelength. This means that if the frequency of a wave increases while maintaining a constant wave speed, the wavelength must decrease, and vice versa. Similarly, if the wavelength increases under constant wave speed, the frequency must decrease.

Understanding this relationship is essential for comprehending various phenomena in physics. For example, within the electromagnetic spectrum, different types of waves—such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays—exhibit varying frequencies and wavelengths. However, they all travel at the same speed: the speed of light.

In summary, the equation

links wave speed ($v$), frequency ($f$), and wavelength ($\lambda$) to demonstrate that wave speed is equal to the product of frequency and wavelength. Essentially, an increase in one variable necessitates a decrease in the other to maintain a constant wave speed. This principle is vital for understanding the behavior of different types of waves, such as light and sound, in various media, making it a cornerstone of physics studies.