Wavelength Calculator
Calculate wavelength as wave speed divided by frequency, for sound, light, and other waves, with unit conversion included.
Wavelength Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser โ no data is sent to any server.
Formula: ฮป = v / f
Worked example โ See calculated output above
Formula
ฮป = v / f
Wavelength equals wave speed divided by frequency.
Worked Examples
Example 1: Basic Example
Problem:Enter sample values to see how Wavelength Calculator works.
Solution:Input your values into the fields and the result appears automatically.
Result:See calculated output above
Example 2: Practical Scenario
Problem:Use real-world values relevant to your physics scenario.
Solution:Adjust the inputs to match your specific needs and review the computed result.
Result:Result updates in real time
Frequently Asked Questions
Why does the same frequency give a different wavelength in air and in water?
Frequency is set by the source and does not change when a wave crosses into a new medium, but the propagation speed does. Sound travels at roughly 343 m/s in air near room temperature and about 1480 m/s in fresh water, so a 1000 Hz tone has a wavelength close to 0.34 m in air and near 1.5 m in water. Enter the speed for the medium you actually care about.
What wave speed should I enter for light or radio waves?
For electromagnetic waves in vacuum use the speed of light, 299792458 m/s, which is close enough to 3e8 for most work. A 100 MHz FM carrier therefore has a wavelength of about 3 m. Inside a dielectric the speed drops by the refractive index, so light of a given frequency has a shorter wavelength in glass than in air.
How are wavelength, period and frequency related?
Period is the reciprocal of frequency, T = 1/f, and it is the time for one full cycle to pass a fixed point. Because the wave advances one wavelength in one period, lambda = v x T, which is the same relation as lambda = v/f. If you have measured a period on an oscilloscope, invert it first to obtain frequency in hertz before using Wavelength Calculator.
What is wavenumber and how does it follow from the wavelength?
The angular wavenumber is k = 2 x pi / lambda, in radians per metre, and it appears in wave equations of the form cos(kx - wt). Spectroscopists more often quote the spectroscopic wavenumber, simply 1/lambda, usually in reciprocal centimetres. Both are inverse lengths, so a shorter wavelength always means a larger wavenumber and higher photon energy.
How does wavelength set the size of an antenna?
Resonant antennas are sized in fractions of a wavelength: a half-wave dipole is about lambda/2 long and a quarter-wave monopole about lambda/4 above a ground plane. At 100 MHz the free-space wavelength is roughly 3 m, so a quarter-wave element is near 0.75 m. Real elements are cut slightly short because the velocity factor of the conductor shortens the effective wavelength.
Why does the wavelength of a fixed musical note change with air temperature?
The speed of sound in air rises with temperature, by roughly 0.6 m/s for every degree Celsius near room conditions, giving about 343 m/s at 20 C. Since frequency is fixed by the vibrating source, a warmer room stretches the wavelength. This is why wind instruments and organ pipes, whose pitch depends on the wavelength that fits the pipe, drift sharp as they warm up.
How does wavelength relate to the modes of a string or a pipe?
A standing wave must fit the boundary conditions. A string fixed at both ends supports wavelengths of 2L/n for integer n, as does a pipe open at both ends. A pipe closed at one end supports 4L/n for odd n only, so its fundamental is an octave lower than an open pipe of the same length and it produces only odd harmonics.
How do I work backwards from a measured wavelength to the frequency?
Rearrange lambda = v/f to give f = v/lambda, using the wave speed of the medium. A ripple with a 0.5 m crest-to-crest spacing travelling at 2 m/s has a frequency of 4 Hz. The same rearrangement gives the wave speed from a known frequency and wavelength, which is how the speed of sound is measured in a resonance tube experiment.
Why do low-frequency sounds bend around obstacles more than high-frequency ones?
Diffraction is strong when the wavelength is comparable to or larger than the obstacle. In air a 20 Hz tone has a wavelength above 17 m and spreads easily around walls and furniture, while a 10 kHz tone is only about 34 mm long and casts a pronounced acoustic shadow. That mismatch is why bass leaks through doorways while treble stays directional.
What is dispersion, and does it break the lambda = v/f relationship?
The relation always holds, but in a dispersive medium the wave speed itself depends on frequency, so you must enter the speed at the frequency of interest rather than a single constant. Deep-water gravity waves, optical fibres and many solids are dispersive. Dispersion is what smears a short optical pulse as it travels and what separates white light into colours in a prism.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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