Calculate sound frequency from wavelength and air temperature, or wavelength from frequency using the speed of sound in air and unit conversions.

Approximate sound waves in dry ideal air: c = 331โˆš(T/273.15) m/s. Temperature alone does not determine frequency; wavelength or frequency is also required. This fixed-composition model omits humidity, wind and real-gas effects and is unsuitable near phase changes or extreme temperatures.

Frequency From Temperature Formula

This calculator estimates sound frequency from wavelength and air temperature, or wavelength from sound frequency. It uses the approximate dry-air relation c = 331โˆš(T/273.15) m/s. Temperature alone does not determine frequency. For a fixed source in stationary air, temperature changes speed and wavelength, not the source frequency. Humidity, wind, extreme temperatures and real-gas effects are outside this model.

f = (331 ร— SQRT (T / 273.15)) / w

Variables:

  • f is sound frequency (Hz)
  • T is the temperature (K) 
  • w is the wavelength (m) 

Convert temperature to kelvin, divide by 273.15, take the square root and multiply by 331 m/s to estimate sound speed; then divide by wavelength in meters. To find wavelength instead, divide sound speed by frequency in Hz. Enter the actual air temperature; an empty field does not silently assume 20ยฐC.

Temperature (ยฐC) to Frequency (Hz) Conversion Table (Assumes ฮป = 1.00 m; c = 331 ร— โˆš(T/273.15))
Temperature (ยฐC) Frequency (Hz)
-20318.7
-10324.9
0331.0
5334.0
10337.0
15340.0
20342.9
22344.1
25345.8
30348.7
35351.6
37352.7
40354.4
50360.0
60365.6
70371.0
80376.4
90381.7
100386.9
120397.1
*Assumes plane wave at fixed wavelength ฮป = 1.00 m. Speed of sound c = 331 ร— โˆš(T/273.15) m/s with T in kelvin; Frequency f = c / ฮป.

How to Calculate Frequency From Temperature?

The following steps outline how to calculate the Frequency From Temperature.

  1. First, determine the temperature (K). 
  2. Next, determine the wavelength (m). 
  3. Next, gather the formula from above: f = (331 * SQRT ( T/273.15)) / w.
  4. Finally, calculate the Frequency From Temperature.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

temperature (K) = 303

wavelength (m) = 17

f = 331โˆš(303/273.15) / 17 โ‰ˆ 20.5069 Hz.