Wave Speed Calculator
Wave Speed Calculator
Waves transport energy through a medium (or through vacuum, in the case of light) without transporting matter. Three quantities describe any periodic wave: its speed v, its frequency f (how many cycles pass per second), and its wavelength λ (the distance between successive crests). They are linked by the universal wave relation v = fλ. Our Wave Speed Calculator solves for any one of the three when you know the other two, making it useful for sound, light, radio, and water waves alike.
What Is Wave Speed?
Wave speed is how fast a crest travels, measured in meters per second (m/s). Sound in air travels about 343 m/s; light in vacuum travels 299,792,458 m/s.
What Is Frequency and Wavelength?
Frequency (Hz) counts cycles per second. Wavelength (m) is the spatial period of the wave. Higher frequency means shorter wavelength when speed is fixed.
A fourth quantity, the period T, ties frequency and wavelength together: T = 1/f is the time for one full cycle, and the wavelength is the distance the wave travels in one period, λ = v·T. This is why v = fλ is sometimes written v = λ/T — speed equals one wavelength covered per period. Understanding all three (f, λ, T) helps when a problem gives you the period instead of the frequency: just take its reciprocal before using the calculator.
Pick what to solve for with the Solve For radio buttons, enter the two known values, and click Calculate.
Solve for Wave Speed
- Enter Frequency in Hz.
- Enter Wavelength in m.
- Click Calculate → Speed in m/s.
Worked Example 1: A 440 Hz Tone in Air (343 m/s)
First find wavelength: λ = 343 / 440 ≈ 0.78 m. Then speed = 440 × 0.78 ≈ 343 m/s (consistent). If you instead enter f = 440 and λ = 0.78, speed = 343.2 m/s.
Solve for Frequency
- Enter Wave Speed in m/s.
- Enter Wavelength in m.
- Click Calculate → Frequency in Hz.
Worked Example 2: Sound of Wavelength 1 m in Air
f = 343 / 1 = 343 Hz, a musical note close to F4.
Solve for Wavelength
- Enter Wave Speed in m/s.
- Enter Frequency in Hz.
- Click Calculate → Wavelength in m.
Worked Example 3: 100 MHz FM Radio (v = c)
λ = 299,792,458 / 100,000,000 ≈ 2.998 m. FM antennas are sized to this wavelength.
Edge Cases
- Zero frequency or wavelength → speed is 0 (or undefined mode).
- Zero speed → frequency or wavelength becomes 0.
- Extremely high frequency (light) gives tiny wavelengths in the nanometer range.
- Negative values rejected: physical wave quantities here are non-negative.
Worked Example 4: A Guitar String's Fundamental (v = 400 m/s, f = 110 Hz)
λ = v/f = 400/110 ≈ 3.64 m. The wavelength on the string is far longer than the string itself because only a fraction of the wave fits as the standing-wave fundamental; the full pattern is twice the string length. This shows how the same relation applies to waves on strings, where speed depends on tension and linear density rather than a surrounding medium.
Worked Example 5: Ultrasound in Tissue (v = 1540 m/s, f = 2 MHz)
λ = 1540 / 2,000,000 = 7.7 × 10⁻⁴ m = 0.77 mm. The tiny wavelength is what gives medical ultrasound its fine imaging resolution — short wavelengths resolve small structures.
Worked Example 6: Ocean Swell (v = 8 m/s, λ = 40 m)
f = v/λ = 8/40 = 0.2 Hz, a period of 5 s between crests. Long-wavelength ocean swells arrive slowly but travel fast over great distances.
The fundamental wave relation:
Solving for the other variables:
This holds for any linear wave (sound, light, water) as long as the medium is uniform and dispersion is ignored.
For sound specifically, the speed depends on the medium's properties: in an ideal gas v = √(γRT/M), so it rises with temperature and falls with molecular mass. In a string, v = √(T/μ) where T is tension and μ is mass per unit length. In deep water, gravity waves have v ≈ √(gλ/2π), which means longer wavelengths travel faster — a dispersive case where the simple single-speed assumption breaks down. The calculator uses one speed you supply; for dispersive media, pick the speed that matches your wavelength of interest.
Wave speed for a fixed wavelength of 1 m at various frequencies:
| Frequency (Hz) | Wave Speed (m/s) |
|---|---|
| 100 | 100 |
| 343 | 343 |
| 1000 | 1000 |
| 440 | 440 |
| 20000 | 20000 |
Speed scales linearly with frequency when wavelength is constant.
Frequency for sound (v = 343 m/s) at various wavelengths:
| Wavelength (m) | Frequency (Hz) |
|---|---|
| 0.5 | 686 |
| 1 | 343 |
| 2 | 171.5 |
| 5 | 68.6 |
| 10 | 34.3 |
Frequency is inversely proportional to wavelength: doubling the wavelength halves the frequency.
Wavelength of light (v = c) at various frequencies:
| Frequency (Hz) | Wavelength (m) |
|---|---|
| 4.0e14 | 7.49e-7 |
| 5.0e14 | 5.99e-7 |
| 6.0e14 | 4.99e-7 |
| 7.5e14 | 3.99e-7 |
| 1.0e15 | 2.99e-7 |
Visible light spans roughly 400-700 nm; higher frequency means shorter (bluer) wavelength.
The same inverse wavelength-frequency pattern appears in the sound table: as wavelength grows from 0.5 m to 10 m, frequency drops from 686 Hz to 34.3 Hz, sliding from the mid-range down to the low bass humans can barely hear. This is why bass speakers (woofers) are large — they must move air over long wavelengths — while tweeters handle the short, high-frequency waves.
- Match the medium's speed: use 343 m/s for sound in air, 1500 m/s in water, c for light.
- Watch units: frequency in Hz, wavelength in m, speed in m/s. Convert cm or kHz first.
- Sound vs light: sound needs a medium; light does not, but both obey v = fλ.
- Musical notes: A4 = 440 Hz; its wavelength in air is about 0.78 m.
- Radio design: antenna length is often λ/4 or λ/2 of the broadcast frequency.
- Check the mode: select the correct variable to solve for before entering numbers.
- Temperature affects sound: sound speed in air rises about 0.6 m/s per °C. At 0°C it is ~331 m/s; at 20°C about 343 m/s. Use the value matching your conditions.
- Use the right c for light: in vacuum c = 299,792,458 m/s, but in glass or water light slows (refractive index n > 1), so use v = c/n for those media.
- Convert kHz and MHz: radio and audio frequencies are often given in kilo- or megahertz; multiply by 10³ or 10⁶ before entering Hz.
- String and water speeds differ: don't assume 343 m/s for every wave — a guitar string or ocean wave uses a completely different speed determined by tension/density or gravity.
- Reciprocal of period: if a problem gives period T instead of frequency, enter f = 1/T.
- Non-dispersive assumption: in dispersive media, speed depends on frequency, so v = fλ applies instantaneously but λ shifts across the spectrum.
- Uniform medium: speed is taken as constant; refraction at boundaries changes direction and speed.
- Linear waves: very high amplitudes can break the simple relation.
- No attenuation: energy loss over distance is ignored.
- Si units only: enter values already in Hz, m, m/s.
- Phase vs group velocity: in dispersive media a wave packet travels at group velocity, which can differ from the phase speed used in v = fλ.
- No Doppler shift: the calculator gives the intrinsic relation in a stationary medium; a moving source or observer changes the observed frequency, not this formula.
- Amplitude independence: for small amplitudes the speed is set by the medium, not by how tall the wave is; very large waves can behave nonlinearly.
What is the wave speed formula?
v = fλ, where v is speed, f is frequency, and λ is wavelength.
What is the speed of sound in air?
Approximately 343 m/s at 20°C, though it varies slightly with temperature and humidity.
How do I find wavelength from frequency?
λ = v / f. For light, use c ≈ 299,792,458 m/s.
Can this be used for light?
Yes. Use the speed of light c for the wave speed; results give optical wavelengths.
Why does higher frequency mean shorter wavelength?
Because v = fλ is constant for a fixed medium; if f rises, λ must fall to keep the product constant.
What unit is frequency measured in?
Hertz (Hz), equal to one cycle per second.
Is wavelength the same as period?
No. Period is time per cycle (T = 1/f); wavelength is distance per cycle (λ = vT).
What is a typical radio wavelength?
FM 100 MHz has λ ≈ 3 m; this is why car antennas are roughly that size.
Does wave speed depend on amplitude?
In ideal linear waves, no. Real large-amplitude waves can show amplitude-dependent speed.
Can I calculate water wave speed?
Yes, using the appropriate wave speed for the water depth and gravity, but shallow-water and deep-water speeds differ; this calculator uses the simple v = fλ relation.
What is the period of a wave?
The period T = 1/f is the time for one cycle to pass a point. Wavelength is the distance covered in that time, so λ = v·T.
Does sound travel faster in water than air?
Yes. Sound moves about 1500 m/s in water versus ~343 m/s in air because water is denser and less compressible, which transmits pressure disturbances faster.
Why do I need frequency to find wavelength?
Because λ = v/f — without knowing how often crests repeat (frequency), you cannot know the distance between them (wavelength) for a given speed.
Can two waves have the same speed but different frequencies?
Yes, in a non-dispersive medium (like air for sound). They then have different wavelengths, since λ = v/f and v is fixed.
How is wave speed used in music?
The pitch (frequency) of a note depends on the wavelength set by the instrument and the wave speed on the string or in the air column; longer strings or tubes produce lower frequencies.
Last updated: July 18, 2026
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