Chapter One: An Acoustics Primer

6. What is wavelength?

Frequency is directly related to wavelength, which is represented by the Greek letter lambda (λ). Wavelength is the spatial distance required to complete one full cycle of a traveling wave.

wavelength graph

The formula for wavelength in air* is:

wavelength formula

Because a sound wave propagates through space at the speed of sound, these calculations use consistent units (inches, feet, meters, etc.).

Examples: an A440 Hz waveform (the pitch most modern orchestras tune to) in dry, 20°C (68°F) air would create a wavelength that is:

≈30.7 inches (≈13,504 inches/sec ÷ 440 Hz)
≈2.6 feet (≈1128 ft/sec ÷ 440 Hz)
≈0.8 meters (≈344 m/s ÷ 440 Hz)

Notice that if the speed of sound changes with temperature, humidity, or propagation medium, the wavelength changes accordingly.

Wavelength is inversely proportional to frequency. In other words, the higher the frequency, the shorter the wavelength. For example, within the human hearing range, a 20 Hz airborne wave has a wavelength just over 56 ft, whereas a 20 kHz wave has a wavelength of approximately 0.7 in.

Bell X-1
Wavelength Calculator

Enter a frequency in Hz:

hertz (Hz)

The wavelength for the input frequency in air at 20°C with 0% humidity is approximately:

inches
centimeters
feet
meters
cubits
*For the wavelength of electromagnetic waves such as radio signals or light waves, simply substitute the speed of light (≅300,000 km/s) for the speed of sound in the fomula above. Visible light waves, whose frequencies span roughly 430–750 terahertz (THz), are so short, they are often measured in ångströms, which is one 10-billionth of a meter long, i.e. many orders of magnitude shorter than typical sound wavelengths.