Sound Wavelength Calculator
Convert between the frequency of a sound (Hz) and its wavelength (m). The half wavelength, the quarter wavelength and the period are shown too. The speed of sound comes from the air temperature, in °C or °F.
How wavelength and frequency are calculated
Frequency, wavelength and the speed of sound are linked:
- Wavelength (m) = speed of sound (m/s) ÷ frequency (Hz)
- Frequency (Hz) = speed of sound (m/s) ÷ wavelength (m)
- Period (seconds) = 1 ÷ frequency (Hz)
Frequency is how many times the wave repeats in one second. The wavelength is the length of one wave, and the period is the time one wave takes.
The speed of sound
The speed of sound is calculated with this approximate formula:
- Speed of sound (m/s) ≈ 331.5 + 0.6 × temperature (°C)
It gives 343.5 m/s at 20 °C (68 °F). This formula uses the temperature only; humidity, pressure and wind are not considered. It is a value for air, and the real speed of sound varies a little with those conditions. You can enter temperatures from −50 °C to 60 °C (−58 °F to 140 °F).
If you choose °F, the temperature is converted exactly to °C with °C = (°F − 32) × 5 ÷ 9 before the calculation. The line under the temperature box shows the temperature used in both units, so you can check it. For example, 68 °F gives the same result as 20 °C.
Examples (20 °C, speed of sound 343.5 m/s)
| Frequency | Wavelength | Half wavelength | Quarter wavelength |
|---|---|---|---|
| 20 Hz | 17.175 m | 8.5875 m | 4.29375 m |
| 100 Hz | 3.435 m | 1.7175 m | 0.85875 m |
| 1 kHz | 0.3435 m | 0.17175 m | 0.085875 m |
| 10 kHz | 0.03435 m | 0.017175 m | 0.0085875 m |
| 20 kHz | 0.017175 m | 0.0085875 m | 0.00429375 m |
Low sounds have long wavelengths and high sounds have short ones.
Using the half and quarter wavelength
The half and quarter wavelengths are rough guides when you think about reflection and interference.
- At a frequency where the path difference between the direct sound and a sound reflected from a wall is half a wavelength, the two sounds tend to cancel each other.
- When a speaker is placed away from a wall, the path difference with the reflected sound is twice the distance to the wall. So cancellation tends to happen at the frequency where the distance to the wall is a quarter wavelength.
A real room has many reflecting surfaces and more complicated conditions. Use these values only as a guide.
Notes
- The frequency and the wavelength must be greater than 0, with decimals allowed (up to 12 digits before the decimal point and 6 decimal places). The frequency can be up to 1,000,000 Hz (1,000 kHz). Use a period as the decimal separator; commas are accepted only as thousands separators.
- People are generally said to hear from about 20 Hz to 20 kHz. The tool also calculates outside that range.
- To find how long sound takes to travel a distance, see the Speaker Delay Calculator. For converting a frequency to a period or back, see the Frequency ⇄ Period Converter.
Frequently asked questions
What is the wavelength of 100 Hz?
3.435 m at 20 °C (about 11.27 ft). It is the speed of sound (343.5 m/s) divided by the frequency (100 Hz).
How many Hz is 1 kHz?
1 kHz = 1,000 Hz. The prefix k (kilo) means 1,000 times.
Does the wavelength change with temperature?
Yes. Sound is faster in warmer air, so the same frequency has a longer wavelength. For 1 kHz the wavelength is 0.3315 m at 0 °C, 0.3435 m at 20 °C and 0.3555 m at 40 °C.
What is the period?
The time one wave takes. It is the reciprocal of the frequency; for 1 kHz it is 1 ms.