Decibel Shield
Frequency to wavelength calculator
Wavelength is speed divided by frequency. Sound in dry air at 20 °C travels at about 343 m/s, so 1 kHz has a wavelength of 34.3 cm and 100 Hz of 3.43 m. Radio and light travel at 299,792,458 m/s, so 100 MHz is about 3 m. Choose what the wave travels through and enter a frequency; the calculator also gives the half and quarter wavelength, and converts a wavelength back to a frequency.
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Wavelength at 1 kHz · 343.38 m/s
34.34 cm
- Half: 17.17 cm
- Quarter: 8.585 cm
Wavelength to frequency
1 m is the wavelength of 343.4 Hz
Wavelength = speed ÷ frequency. Sound in dry air uses the temperature you set; radio and light use the exact speed of light.
Wavelength of sound in air
| Frequency | Wavelength | Half | Quarter |
|---|---|---|---|
| 20 Hz | 17.2 m | 8.58 m | 4.29 m |
| 31.5 Hz | 10.9 m | 5.45 m | 2.73 m |
| 50 Hz | 6.87 m | 3.43 m | 1.72 m |
| 63 Hz | 5.45 m | 2.73 m | 1.36 m |
| 100 Hz | 3.43 m | 1.72 m | 85.8 cm |
| 125 Hz | 2.75 m | 1.37 m | 68.7 cm |
| 250 Hz | 1.37 m | 68.7 cm | 34.3 cm |
| 500 Hz | 68.7 cm | 34.3 cm | 17.2 cm |
| 1 kHz | 34.3 cm | 17.2 cm | 8.58 cm |
| 2 kHz | 17.2 cm | 8.58 cm | 4.29 cm |
| 4 kHz | 8.58 cm | 4.29 cm | 2.15 cm |
| 8 kHz | 4.29 cm | 2.15 cm | 1.07 cm |
| 10 kHz | 3.43 cm | 1.72 cm | 8.58 mm |
| 16 kHz | 2.15 cm | 1.07 cm | 5.37 mm |
| 20 kHz | 1.72 cm | 8.58 mm | 4.29 mm |
Wavelength of radio waves
| Frequency | Wavelength | Quarter |
|---|---|---|
| 1 MHz | 300 m | 74.9 m |
| 10 MHz | 30 m | 7.49 m |
| 100 MHz | 3 m | 74.9 cm |
| 1 GHz | 30 cm | 7.49 cm |
| 2.4 GHz | 12.5 cm | 3.12 cm |
| 5 GHz | 6 cm | 1.5 cm |
| 10 GHz | 3 cm | 7.49 mm |
The formula
λ = v / f, and f = v / λ. For sound in dry air, v = 331.46 × √(1 + T / 273.15) m/s with T in °C, which is the speed of sound calculator's formula. For radio and light, v is the speed of light, fixed at exactly 299,792,458 m/s by the definition of the metre. To turn a frequency into the length of one cycle in time rather than in space, use Hz to ms.
Sources: NIST CODATA, speed of light in vacuum; BIPM, SI base unit: metre; OpenStax University Physics, 17.3 Speed of Sound; HyperPhysics, Sensitivity of Human Ear; UIUC Physics 406, Acoustics of Small Rooms; Haus & Melcher, Electromagnetic Fields and Energy, 12.7 (MIT); ITU-R Recommendation P.453-14, The radio refractive index.
How do you convert frequency to wavelength?
Divide the speed of the wave by its frequency: λ = v / f. For sound in air at 20 °C the speed is about 343 m/s, so 343 Hz has a wavelength of 1 m. For radio and light it is 299,792,458 m/s, so 300 MHz is almost exactly 1 m. Use metres per second and hertz and the answer is in metres.
What is the wavelength of 20 Hz and of 20 kHz?
In air at 20 °C, 20 Hz has a wavelength of about 17.2 m and 20 kHz about 1.7 cm. Those are the two ends of the range usually given for human hearing, so audible sound spans wavelengths about a thousand times apart, from longer than a bus to shorter than a fingernail.
Does temperature change the wavelength of a sound?
Yes, because it changes the speed. A tone keeps its frequency, but in warm air sound travels faster, so each cycle is a little longer: a 1 kHz tone is about 33.1 cm long at 0 °C and 34.9 cm at 30 °C. The calculator takes the air temperature for that reason.
Why give the half and quarter wavelength?
They are the lengths that matter in rooms and antennas. Between two parallel walls the lowest standing wave (room mode) fits half a wavelength across the room, so a wall 3.4 m away from its opposite sets up a mode near 50 Hz. A quarter-wave antenna is a quarter of the radio wavelength long.
