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.

#### Tips and warnings

- 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.

#### References

- "Physics for Scientists & Engineers With Modern Physics"; Douglas C. Giancoli; 2008
- Hampden-Sydney College; Astronomy 105: Wavelength-Frequency Relationship; Hans Krim; 1997
- The Engineering Toolbox; Sound Frequency, Wavelength and Octave: An Introduction to the Nature of Sound
- San Jose State University; Sound Waves
- Indiana University; How Fast Does Sound Travel?