How long is a 440 Hz sound wave? 77.95 cm in air, 3.37 m in water. Find frequency, wavelength or wave speed from the other two, with the period, angular frequency and nearest piano key.
How long is a 100 Hz sound wave in air?
How long is a 440 Hz sound wave? 77.95 cm in air, 3.37 m in water. Find frequency, wavelength or wave speed from the other two, with the period, angular frequency and nearest piano key.
The calculator below is set to find the wavelength of a 100 Hz sound traveling through air at 20 °C, where sound moves at 343 m/s, or 1,125 ft/s. The wavelength is that speed divided by 100, and the result gives it in metric and US units along with the period, the angular frequency and the nearest key on a piano.
The air setting matters. Sound speeds up as air warms, by about 0.6 m/s for every degree Celsius, so the same tone has a slightly longer wavelength on a hot day. People hear roughly 20 Hz to 20 kHz, and the table in the result shows how much longer the same 100 Hz wave becomes in water, iron or diamond.
Measuring in a different medium or at another temperature? Pick another preset, or choose to type your own speed.
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How long a sound wave really is
How far apart are the crests of concert A? In air at 20 °C, 77.95 cm, a little over 2.5 ft. Play the same 440 Hz under water and they spread to 3.37 m, because sound moves more than four times faster there. This calculator solves v = f × λ for whichever of the three you are missing, using seven preset speeds or your own, and adds the period, the angular frequency, the wavenumber and the nearest piano key.
Two numbers in, the third one out
- Find the - frequency, wavelength or wave speed. The boxes below change to ask only for the other two.
- Wave travels through - for frequency or wavelength, pick air, fresh water, seawater, soft tissue, granite, iron or diamond, or Type my own speed with its unit (m/s, ft/s, mph, km/h or km/s).
- Frequency - the value and its unit, Hz to GHz. Concert A is 440 Hz.
- Wavelength - crest to crest, in mm, cm, m, km, inches or feet.
- Read the result - the answer in metric and US units, the period, ω and k, whether people can hear it, the nearest piano key, and a table of the same wave in all seven media.
Why the medium moves the wavelength but not the pitch
A wave's frequency belongs to whatever makes it. A tuning fork vibrates 440 times a second whether it rings in a hall or a swimming pool, and each vibration sends out one wave. What the medium decides is how fast those waves travel away, and so how much room each one takes up. Fast medium, long waves. Slow medium, short ones. Pitch follows frequency, which is why the note sounds like A in both places while its wavelength differs by a factor of 4.318.
The speeds in the presets come from the Wikipedia article on the speed of sound: 343 m/s in dry air at 20 °C, 1,481 m/s in fresh water at the same temperature, about 1,500 m/s in seawater, 5,120 m/s in iron and 12,000 m/s in diamond. Granite, about 5,000 m/s, is from the article on seismic waves, and 1,540 m/s is the value medical ultrasound scanners assume for soft tissue when they turn an echo's travel time into depth. Air is what physicists call non-dispersive: every audible frequency travels at practically the same speed, so one preset serves the whole range.
The three extra numbers are different views of the same wave. The period is the time one cycle takes, 1 / f, so 2.27 ms at 440 Hz. The angular frequency ω = 2πf, 2,764.60 rad/s for the same note, is the form most textbook equations of motion use. The wavenumber k = 2π / λ, 8.06 rad/m in air, counts radians of phase per meter of travel.
Wavelengths from a one-hertz rumble to an ultrasound scan
Every row is the calculator's own output. Across the table the wavelength shrinks by a factor of more than fifty million, and the top and bottom rows are both sound.
| Wave | Frequency | Medium | Wavelength | US units |
|---|---|---|---|---|
| Slow ground vibration | 1 Hz | granite | 5.00 km | 3.11 mi |
| Lowest audible tone | 20 Hz | air | 17.15 m | 56.27 ft |
| Lowest piano key, A0 | 27.5 Hz | air | 12.47 m | 40.92 ft |
| Middle C, C4 | 261.63 Hz | air | 1.31 m | 4.30 ft |
| Concert A, A4 | 440 Hz | air | 77.95 cm | 2.56 ft |
| Concert A | 440 Hz | iron | 11.64 m | 38.18 ft |
| Highest piano key, C8 | 4,186.01 Hz | air | 8.19 cm | 3.23 in |
| Top of human hearing | 20 kHz | air | 1.72 cm | 0.68 in |
| Top of a dog's hearing | 45 kHz | air | 7.62 mm | 0.30 in |
| Top of a cat's hearing | 79 kHz | air | 4.34 mm | 0.17 in |
| Highest bat hearing quoted | 200 kHz | air | 1.72 mm | 0.0675 in |
| Deep-organ ultrasound | 1 MHz | soft tissue | 1.54 mm | 0.0606 in |
| Upper end for deep organs | 6 MHz | soft tissue | 256.67 µm | 0.0101 in |
| Superficial ultrasound | 18 MHz | soft tissue | 85.56 µm | 0.0034 in |
Hearing limits for dogs (67 Hz to 45 kHz), cats (55 Hz to 79 kHz) and some bat species (up to 200 kHz) are as given in Wikipedia's hearing range article; the ultrasound bands of 1 to 6 MHz for deep organs and 7 to 18 MHz for structures near the skin are from its medical ultrasound article.
One kilohertz, seven materials
A 1 kHz tone keeps its frequency everywhere, so the wavelength column is simply each speed divided by 1,000.
| Medium | Speed | Wavelength of 1 kHz |
|---|---|---|
| Air at 20 °C | 343 m/s (1,125.33 ft/s) | 34.30 cm (1.13 ft) |
| Fresh water at 20 °C | 1,481 m/s (4,858.92 ft/s) | 1.48 m (4.86 ft) |
| Seawater | 1,500 m/s (4,921.26 ft/s) | 1.50 m (4.92 ft) |
| Soft tissue | 1,540 m/s (5,052.49 ft/s) | 1.54 m (5.05 ft) |
| Granite | 5,000 m/s (16,404.20 ft/s) | 5.00 m (16.40 ft) |
| Iron | 5,120 m/s (16,797.90 ft/s) | 5.12 m (16.80 ft) |
| Diamond | 12,000 m/s (39,370.08 ft/s) | 12.00 m (39.37 ft) |
Numbers about waves that tend to surprise
Who types a frequency into this
Wave questions with the arithmetic shown
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Calculator verified by the LiczGrupa.pl team
Content, formulas and results have been reviewed for accuracy and relevance by our team of specialists.
Reviewed by: Natalia Skrzek