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How to Calculate Frequency From Wavelength

Updated April 17, 2017

Both sound and light (in most circumstances) travel in waves. Scientists measure the frequency, wavelength and velocity of these waves. The relationship among the three variables is simple. The velocity of a wave equals the frequency of the wave times the wavelength of the wave. This relationship makes it easy to determine the frequency of a soundwave or a lightwave from its known wavelength.

Determine the wavelength of the light. For example, a visible blue light has a wavelength of approximately 460 nanometres.

Divide the light's wavelength by 1 x 10^9 to find the wavelength in meters. In the example, 460/(1 x 10^9) = 4.6 x 10^-7.

Divide the speed of light, 3.00 x 10^8 meters per second, by the wavelength in meters. In the example, (3.00 x 10^8)/(4.6 x 10^-7) = 6.52 x 10^14.

Express your answer in the units calculated, which is reciprocal seconds (s^-1). The frequency of the blue light is 6.52 x 10^14 s^-1. This is the same thing as 6.52 x 10^14 Hertz, or Hz.

Determine the wavelength of the sound. For example, the wavelength of middle C on a piano is approximately 1.29m.

Divide the speed of the sound, 343 meters per second, by the wavelength in meters. In the example, 343/1.29 = 266, rounded off.

Express your answer in the units calculated, which is reciprocal seconds (s^-1). The frequency of middle C on a piano is 266 s^-1. This is the same thing as 266 Hz.

Tip

The speed of sound varies, depending on air temperature and humidity. It is 343.4m/s in dry air at 20 degrees Celsius. The speed of light is constant in a vacuum.

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About the Author

John Woloch writes professionally for various websites. He has published in the Dutch journal "Crux" and writes frequently on oil painting, classical languages and topics involving math and biochemistry. Woloch holds a Master of Arts in English from the University of Chicago, a Master of Arts in classics from Ohio State University and a postbaccalaureate pre-medical degree from Georgetown University.