MotionLab

Frequency Calculator

How many wave cycles pass per second, from wave speed and the distance between peaks.

Wave speed (m/s)

Wavelength (m)

Frequency (Hz)

439.744

f = v / λ

What you entered

Wave speed (m/s): 343Wavelength (m): 0.78

1
f = v ÷ λ
343 ÷ 0.78= 439.7436 Hz

Result

Frequency (Hz): 439.744

A 0.78m wave traveling at 343 m/s has a frequency of 439.744 Hz.

Frequency from wave speed and wavelength

Frequency is wave speed divided by wavelength - the inverse of the wavelength calculation.

Wave speed (m/s)	Wavelength (m)	Frequency (Hz)	Wave
343	0.0172	19941.86	Near the top of hearing
343	0.78	439.74	Close to concert A
343	1	343.00	1 metre sound wave
300000000	0.125	2400000000.00	Wi-Fi, 2.4 GHz
300000000	3	100000000.00	FM radio, 100 MHz

Row two gives 439.74 Hz rather than exactly 440, because 0.78 m is a rounded wavelength - a reminder that inverting a rounded figure does not return the original exactly. Frequency and wavelength are inversely proportional at a fixed wave speed, so halving one doubles the other. Frequency is the property that stays constant when a wave crosses into a new medium: light entering glass slows down and its wavelength shortens, but its frequency, and therefore its colour, does not change.

Inverse relationship with wavelength

Frequency and wavelength are inversely related at a fixed wave speed — shorter wavelength always means higher frequency, and vice versa, which is why high-pitched sounds have short wavelengths and low-pitched sounds have long ones.

Frequency also equals 1/period

Frequency can also be calculated as the inverse of the period (time for one full cycle) — both approaches describe the same underlying oscillation, just from different starting measurements.

Frequently asked questions

A sound wave in air has a wavelength of 0.5 m. What frequency is that?

f = v/λ = 343/0.5 = 686 Hz. That's roughly the pitch of a high-pitched speaking voice or the note E5. Human hearing ranges from about 20 Hz (17.15 m wavelength) to 20,000 Hz (0.017 m wavelength).

How are frequency and pitch related?

Frequency directly determines pitch — higher frequency = higher pitch. Concert A is 440 Hz. Each octave doubles the frequency (A5 = 880 Hz, A3 = 220 Hz). The relationship is logarithmic: equal frequency ratios produce equal perceived pitch intervals.

What's the frequency of visible light?

Red light: ~430 THz (700 nm wavelength). Violet: ~750 THz (400 nm). These frequencies are enormous because light travels at 3×10⁸ m/s. See the wavelength calculator to convert between light wavelength and frequency.