Frequency Calculator

Use our frequency calculator to find a wave’s frequency given its length and velocity.




Frequency Formula

𝑓 = 𝑣 / λ
Learn how we calculated this below

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How to Calculate Frequency

Frequency is one of the fundamental concepts in the study of waves, whether they be sound waves, light waves, or any other type. Frequency, denoted as 𝑓, refers to the number of cycles of a wave that pass a fixed point in one second.

It is measured in Hertz (Hz), where one Hertz is equivalent to one cycle per second.

The frequency of a wave is crucial because it determines many of the wave’s characteristics.

For instance, in sound waves, frequency affects the pitch of the sound: higher frequencies correspond to higher pitches and vice versa. In light waves, frequency determines the color of the light.

Relationship Between Frequency, Wavelength, and Velocity

Wave frequency is inherently linked to the wavelength (λ) and the wave velocity (𝑣). The wavelength is the distance between consecutive corresponding points of the same phase on a wave, such as from crest to crest or trough to trough. Wave velocity is the speed at which the wave propagates through a medium.

These three properties are interconnected through a simple, yet fundamental formula in wave physics:

Frequency Formula

The formula that relates wave frequency, wavelength, and wave velocity is given by:

𝑓 = 𝑣 / λ

𝑓 = wave frequency
λ = wavelength
𝑣 = wave velocity

Thus, the frequency of a wave 𝑓 is equal to its velocity 𝑣 divided by its length λ. This relationship is pivotal because it allows us to calculate any one of the three variables if the other two are known.

Graphic showing the frequency formula where the frequency of a wave is equal to its velocity divided by its length.

For example, suppose a sound wave travels through air at a speed of 343 meters per second and has a wavelength of 0.85 meters. Let’s calculate the frequency of the sound wave.

𝑓 = 343 m⁄s / 0.85 m = 403.53 Hz

So, the frequency of the sound wave is about 403.53 Hertz, meaning that roughly 403.53 cycles of the sound wave pass a fixed point each second.