Every wave obeys v = f × λ. Enter a frequency and choose light, sound in air or sound in water to get the wavelength and period.
Enter the frequency in hertz.
Choose the type of wave.
Read the wavelength and period.
Wave equation: λ = v ÷ f
Period: T = 1 ÷ f
Every wave, whether light, radio or sound, has a speed, a frequency and a wavelength, linked by v = fλ. This calculator takes a frequency in hertz, lets you choose the wave type, and returns the wavelength in metres and the period in seconds. It builds in the right speed: about 3 × 10⁸ m/s for light and radio in vacuum or air, 343 m/s for sound in air at 20 °C, and 1480 m/s for sound in water.
It is handy for Class 11 and 12 wave and optics problems, and for practical questions too: how long an FM antenna should be, how wide a Wi-Fi signal's waves are, or why bass notes spread round corners better than treble. Ham radio operators, sound engineers and sonar designers all switch between frequency and wavelength every day.
1. Write the frequency in hertz. Convert kHz by multiplying by 1000, MHz by 10⁶ and GHz by 10⁹.
2. Choose the wave speed v for the medium: about 3 × 10⁸ m/s for electromagnetic waves, 343 m/s for sound in air at 20 °C, 1480 m/s for sound in water.
3. Divide: λ = v ÷ f to get the wavelength in metres.
4. Find the period: T = 1 ÷ f, in seconds.
5. Convert the wavelength into convenient units, such as cm for microwaves or nm for visible light, where 1 nm = 10⁻⁹ m.
A wave repeats itself every wavelength in space and every period in time. In one period T the wave pattern moves forward exactly one wavelength λ. Speed is distance over time, so v = λ ÷ T. Since frequency is the number of cycles per second, f = 1 ÷ T, which gives v = fλ. The relation holds for every kind of periodic wave, from ripples on a pond to gamma rays, and only the speed changes from one kind of wave to another.
When a wave passes from one medium into another, its frequency stays the same, because it is set by the source. The speed changes, so the wavelength must change to match. Light slows down in glass, so its wavelength shrinks there, which is the root of refraction. A sound at 1000 Hz has a wavelength of about 34 cm in air but about 1.5 m in water, since sound travels more than four times faster in water. The calculator's three options show this directly.
The speed of light in vacuum is exactly 299,792,458 m/s, and in air it is only about 0.03% less. Sound is different: its speed in air rises by roughly 0.6 m/s for every °C, so on a 35 °C summer afternoon it is closer to 352 m/s than 343. In water it depends on temperature and salinity. For precise acoustic work, measure or look up the actual speed; for school problems, use the values the question gives.
Tanvi is tuning her harmonium and wants to know the wavelength in air of the A note at 440 Hz on a mild 20 °C day.
Wave speed: v = 343 m/s
λ = v ÷ f: = 343 ÷ 440 = 0.77954545 m
Period: T = 1 ÷ f = 2.2727 × 10^-3 s
Answer: Wavelength 0.77954545 m; Period 2.2727 × 10^-3 s
Entering MHz or GHz values as if they were hertz.
Using the speed of light for sound, or the other way round.
Assuming frequency changes when a wave enters a new medium; it is the wavelength that changes.
Forgetting that sound cannot travel through a vacuum at all.
Quoting visible-light wavelengths in metres without converting to nanometres, which makes them hard to compare.
Class 11 and 12 physics problems on waves, sound and electromagnetic radiation.
Sizing antennas for FM radio, walkie-talkies and Wi-Fi, which are often a quarter or half wavelength long.
Room acoustics and speaker placement, where low notes have wavelengths of several metres.
Sonar and echo-sounding calculations for ships and fishing boats.
Converting between the colour of light in nanometres and its frequency.
What is the wavelength of 2.4 GHz Wi-Fi?
About 12.5 cm.
Why does sound travel faster in water?
Water is much less compressible than air, so vibrations pass on more quickly.