---
title: "The Wave Equation"
description: "Wave speed is frequency times wavelength, used in either direction for sound, ripples and light. Measuring it means timing or counting something real, such as ripples crossing a tank or an echo return"
canonical: https://lightmysky.com/learn/science/the-wave-equation-mt_wmKhTiXt1p
source: https://lightmysky.com/learn/science/the-wave-equation-mt_wmKhTiXt1p.md
retrieved: 2026-09-12
---

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# The Wave Equation

Wave speed is frequency times wavelength, used in either direction for sound, ripples and light. Measuring it means timing or counting something real, such as ripples crossing a tank or an echo returning.

Subject: Science · Area: Waves, Light & Sound · Ages 15 to 16
Page: https://lightmysky.com/learn/science/the-wave-equation-mt_wmKhTiXt1p

## Ready when they can

- Calculates any one of speed, frequency and wavelength from the other two, with units
- Measures the speed of ripples in a tank or of sound in air and reports the method
- Explains why a higher frequency means a shorter wavelength when the speed is fixed

## Lesson: Speed equals frequency times wavelength

A clap sends compressions through air at about 340 metres per second, and the pitch you hear is the frequency while the spacing between compressions is the wavelength. If you know any two of speed, frequency and wavelength, the third drops out of speed equals frequency times wavelength. A 170 Hz tone in air has a wavelength of 2 metres, since 340 divided by 170 is 2.

Every wave carries the same labels. Frequency counts how many waves pass per second in hertz, and period is the seconds per wave, so the two are reciprocals. Pitch follows frequency, and loudness follows amplitude. In a ripple tank you can count ten waves passing a straw, time them, and divide to get the frequency.

**Example.** Ben measures ripples in a tank. He counts 10 waves passing a straw in 5 seconds, so the frequency is 2 Hz. He measures the wavelength as 3 cm, then multiplies to get the speed. Timing an echo over a known distance gives the speed of sound the same way.

**Tip.** When a question fixes the medium, treat the speed as constant and let frequency and wavelength trade off. Higher frequency then means shorter wavelength. Sound is a longitudinal wave that needs a medium, so unlike light it cannot cross empty space.

**Recap.** Three quantities, one link: speed equals frequency times wavelength.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Standard Form](https://lightmysky.com/learn/mathematics/standard-form-mt_GbZZ2xjBTt)
- [Wave Properties & Types](https://lightmysky.com/learn/science/wave-properties-and-types-mt_LxK9OKZQZX)

## Opens up

- [Ultrasound and Echo Sounding](https://lightmysky.com/learn/science/ultrasound-and-echo-sounding-mt_nE1uPfjhX-)
- [The Electromagnetic Spectrum: Uses and Dangers](https://lightmysky.com/learn/science/the-electromagnetic-spectrum-uses-and-dangers-mt_P_NXNSo1zQ)
- [Progressive Waves: Phase and Path Difference](https://lightmysky.com/learn/science/progressive-waves-phase-and-path-difference-mt_RotpycCNF8)
- [Refraction and Lenses](https://lightmysky.com/learn/science/refraction-and-lenses-mt_u8GKuBMmzC)
- [The Doppler Effect and Shock Waves](https://lightmysky.com/learn/science/the-doppler-effect-and-shock-waves-mt_UVfD_coqh6)