Wave Equation Calculator

About the Wave Equation Calculator

The wave equation relates a wave's speed to its frequency and wavelength. Wave speed equals frequency times wavelength.

Enter any two of speed (m/s), frequency (Hz) and wavelength (m); leave the third blank to solve for it.

How to use this calculator

1. Enter the two values you know, such as frequency and wavelength.
2. Choose the variable you want to solve for, wave speed, frequency, or wavelength.
3. Check the units, because the result depends on matching units like \(\text{Hz}\) and \(\text{m}\).
4. Read the answer and the step-by-step work to see how the formula was rearranged.

The formula explained

The formula \(v = f\lambda\) computes wave speed \(v\) by multiplying frequency \(f\) by wavelength \(\lambda\). If you need a different variable, the same equation can be rearranged to \(f = \frac{v}{\lambda}\) or \(\lambda = \frac{v}{f}\).

• v = wave speed, usually measured in \(\text{m/s}\)
• f = frequency, usually measured in \(\text{Hz}\)
• \(\lambda\) = wavelength, usually measured in \(\text{m}\)

Step by step method

1. Write down the formula \(v = f\lambda\).
2. Substitute the values you know into the equation.
3. If you are solving for \(f\) or \(\lambda\), divide both sides by the other known value.
4. Simplify the result and include the correct units.

Worked example

Problem. A wave has frequency \(f = 5\,\text{Hz}\) and wavelength \(\lambda = 2.4\,\text{m}\). Find the wave speed.

1. Use the formula \(v = f\lambda\).
2. Substitute the values, \(v = 5 \times 2.4\).
3. Multiply to get \(v = 12\).

Tips and common mistakes

• Make sure frequency is in \(\text{Hz}\) and wavelength is in \(\text{m}\), so the speed comes out in \(\text{m/s}\).
• If the calculator asks for a missing variable, remember the rearranged forms, \(f = \frac{v}{\lambda}\) and \(\lambda = \frac{v}{f}\), not just the original formula.

Frequently asked questions