Wave Speed, Frequency and Wavelength: Formula and Calculator
The wave equation v = fλ explained with a calculator for wave speed, frequency and wavelength, plus period, sound and light examples, units and common mistakes.
Key takeaways
- Wave speed = frequency × wavelength: v = f × λ.
- Frequency is waves per second (Hz); the period is the time for one wave: T = 1 ÷ f.
- Sound travels at about 343 m/s in air; light and radio at about 300,000,000 m/s.
On this page
The wave equation links three properties of any wave: v = f × λ. Wave speed (v, in metres per second) equals frequency (f, in hertz) multiplied by wavelength (λ, the Greek letter lambda, in metres). It works for ripples on water, sound, light and radio. If you know any two, you can find the third, and the calculator below does it for you with common unit conversions.
The key terms
- Wavelength (λ): the distance from one point on a wave to the same point on the next, such as crest to crest, in metres.
- Frequency (f): the number of waves passing a point each second, in hertz (Hz). 1 Hz is one wave per second.
- Period (T): the time for one complete wave, in seconds. T = 1 ÷ f.
- Amplitude: the maximum displacement from the rest position. It relates to energy (loudness or brightness), not speed.
- Wave speed (v): how fast the wave travels, in metres per second.
The equations
- v = f × λ
- f = v ÷ λ
- λ = v ÷ f
Wave speed calculator
Enter any two values; the third is calculated. Choose a preset speed for sound or light, or type your own.
Wave speed, frequency and wavelength calculator
Enter any two values.
Worked examples
- A musical note: the A above middle C has a frequency of 440 Hz. In air at 20°C, λ = 343 ÷ 440 ≈ 0.78 m.
- FM radio: a station broadcasting at 100 MHz has λ = 300,000,000 ÷ 100,000,000 = 3 m.
- Wi-Fi: at 2.4 GHz, λ = 300,000,000 ÷ 2,400,000,000 = 0.125 m (12.5 cm).
- Water waves: ripples with a wavelength of 0.2 m arrive at 5 per second. v = 5 × 0.2 = 1 m/s.
- Finding frequency: a sound wave in water (1,480 m/s) has a wavelength of 2 m. f = 1,480 ÷ 2 = 740 Hz.
Typical wave speeds
| Wave | Medium | Approximate speed |
|---|---|---|
| Sound | Air at 20°C | 343 m/s |
| Sound | Water | About 1,480 m/s |
| Sound | Steel | About 5,900 m/s |
| Ocean waves | Open sea | Varies with wavelength and depth |
| Light and radio | Vacuum | 299,792,458 m/s |
| Light | Glass | About 200,000,000 m/s |
Sound needs a medium and travels faster in liquids and solids than in air. Light slows down in glass and water, which causes refraction; see Snell’s law.
Transverse and longitudinal waves
- Transverse waves oscillate at right angles to the direction of travel. Examples: light and all electromagnetic waves, and ripples on water.
- Longitudinal waves oscillate along the direction of travel, creating compressions and rarefactions. Example: sound.
What changes when a wave enters a new medium?
The frequency stays the same, set by the source. The speed changes, so the wavelength changes too. When sound passes from air into water, it speeds up and its wavelength gets longer; when light enters glass, it slows and its wavelength gets shorter.
Reading wave graphs
On a displacement–distance graph, the wavelength is the distance between neighbouring peaks, and the amplitude is the height of a peak above the rest line. On a displacement–time graph, the horizontal gap between peaks is the period, T, and the frequency is 1 ÷ T. Only distance graphs show wavelength, so check the axis label before you read off a value.
Measuring the speed of sound
A simple method: stand a measured distance, say 100 m, from a large wall and clap. Time the echo, or clap in rhythm with the echoes and time 20 claps to reduce timing errors. The sound travels there and back, so speed = 2 × distance ÷ time. With 100 m and an echo time of 0.58 s, v = 200 ÷ 0.58 ≈ 345 m/s. Two microphones connected to an oscilloscope give more precise results, and a ripple tank with a strobe light lets you measure water waves in the same way.
Frequency and what we perceive
- Sound: higher frequency means higher pitch. Humans typically hear from about 20 Hz to 20,000 Hz, with the upper limit falling with age.
- Light: frequency determines colour, from red (lower) to violet (higher).
- Moving sources: the frequency you hear changes when the source moves towards or away from you, the Doppler effect.
Common mistakes
- Not converting units. Change kHz, MHz and GHz to Hz, and cm or nm to metres, before calculating.
- Confusing period and frequency. A frequency of 50 Hz means a period of 0.02 s.
- Thinking amplitude affects speed. A louder sound travels at the same speed as a quieter one.
- Assuming frequency changes between media. It’s the wavelength that changes.
- Using the wrong speed for the medium. Sound travels more than four times faster in water than in air.
All the key wave equations appear on our physics formula sheet.
Frequently asked questions
What is the formula for wave speed?
Wave speed equals frequency multiplied by wavelength: v = f × λ.
Does frequency change when a wave changes speed?
No. Frequency is set by the source. When speed changes, the wavelength changes instead.
How fast does sound travel?
About 343 m/s in air at 20°C, faster in warmer air and much faster in water and solids.
Sources
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