--- title: "The wave equation" description: "Wave speed equals frequency times wavelength. Use the equation in either direction for sound, ripples and light. To measure speed, time or count real events, such as ripples crossing a tank or an echo" canonical: https://lightmysky.com/learn/science/the-wave-equation-mt_wmKhTiXt1p source: https://lightmysky.com/learn/science/the-wave-equation-mt_wmKhTiXt1p.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # The wave equation Wave speed equals frequency times wavelength. Use the equation in either direction for sound, ripples and light. To measure speed, time or count real events, 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 For a periodic wave, speed v equals frequency f times wavelength λ: v = fλ. Frequency counts complete cycles per second in hertz. Wavelength is the distance between neighbouring matching parts. In a steady sound tone, pitch is our perception of frequency; the spacing between neighbouring compressions is its wavelength. **Example.** To measure frequency, start a timer at a crest and call it crest zero. Count ten following crest-to-crest intervals, then stop at crest ten. If those ten complete intervals take 4 seconds, f = 10 ÷ 4 = 2.5 Hz. Measuring wavelength independently then lets you calculate speed with v = fλ. Period T is the time for one complete cycle: T = 1 ÷ f. Sound in air is a longitudinal mechanical disturbance. It needs material to carry it and cannot cross a vacuum. The medium requirement comes from being mechanical, not from being longitudinal; transverse mechanical waves need a medium too. *(drawing: To find wavelength, divide speed by frequency. Use compatible units. To find frequency instead, use f = v ÷ λ.)* When a question states that speed is fixed, fλ must stay constant. Doubling frequency halves wavelength. Do not infer fixed speed from the material alone: temperature, rope tension or frequency-dependent behaviour can affect speed. Use the stated fixed-speed assumption. **Example.** For an echo, measure distance d to a reflector and time from the original clap to its returning echo. Sound travels out and back, so v = 2d ÷ t. At d = 60 m and t = 0.4 s, v = 120 ÷ 0.4 = 300 m/s. A clap supplies a pulse for timing, not a single-frequency tone. Record and repeat measurements to reduce timing uncertainty. **Recap.** Wave speed equals frequency times wavelength. *Original lesson and practice questions written for this learning dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Wave properties & types](https://lightmysky.com/learn/science/wave-properties-and-types-mt_LxK9OKZQZX) ## Optional connections - [Standard Form](https://lightmysky.com/learn/mathematics/standard-form-mt_GbZZ2xjBTt) ## 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)