Waves (v = fλ) Calculator

Solve v = fλ for wave speed, frequency or wavelength from the other two. One button sets v to the speed of light for electromagnetic waves.

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What it asks for

The formula

v = f λ   (the wave equation)
f = 1 / T   and   T = 1 / f
ω = 2πf   (angular frequency, rad/s)
k = 2π / λ   (wave number, rad/m)
v = ω / k   (the same equation, written in ω and k)

From the article The Wave Equation v = fλ — Sound and Light Examples.

Worked example

Question: A tuning fork of frequency 680 Hz is sounded in air where the speed of sound is 340 m/s. Find the wavelength and the time period.

Wavelength: λ = v / f = 340 ÷ 680 = 0.5 m

Check: f = v / λ = 340 ÷ 0.5 = 680 Hz. ✔

Time period: T = 1 / f = 1 ÷ 680 = 0.001470 s, i.e. 1.47 ms

A sanity check worth doing every time: half a metre is a believable wavelength for a fairly high musical note. If you had got 500 m or 0.0005 m, something went wrong.

Worked in full in The Wave Equation v = fλ — Sound and Light Examples.

Learn the method

About this tool

This is one of the tools in the Chemistry Calculator Suite, a free calculator built for IIT-JAM, CSIR-NET, GATE and CUET (Chemical Science) preparation. Nothing is behind a login and no result is stored on a server — the arithmetic runs in your own browser.

The Waves (v = fλ) calculator above is the live tool — type your values and press its button; the answer appears in the same box. The link under it opens the full suite with this tool already selected, next to the others.

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