Wave Speed Calculator
Wave speed from frequency and wavelength (v = fλ).
About this calculator
This calculator applies the fundamental wave equation, v = fλ, which holds for any periodic wave — sound, light, water, or a wave on a string — as the simple statement that speed equals how many wavelengths pass a point each second. From frequency alone it derives the period (T = 1/f, the time for one full cycle) and angular frequency (ω = 2πf, the rate of phase change used in wave equations), and from wavelength it derives the wave number (k = 2π/λ, the spatial analog of angular frequency). To make the resulting speed tangible, it also expresses it as a Mach number relative to the speed of sound in air at room temperature (343 m/s), and converts it to km/h and mph.
Importantly, this calculator only relates frequency, wavelength, and speed to each other — it does not derive wave speed from the medium's physical properties. For a wave on a string, actual speed depends on tension and mass density (v = √(T/μ)); for sound, it depends on air temperature and composition; for light, it's fixed at roughly 3×10⁸ m/s in vacuum. A common mixup is assuming this calculator tells you the propagation speed of sound or light in some medium — it doesn't derive that from physical properties; it simply computes v = fλ from the frequency and wavelength you already know, so if either of those numbers is itself an assumption (like the default 440 Hz standard concert pitch, A4), the wave speed output inherits that assumption.
Inputs
Results
Wave Speed (m/s)
343.2
How to Use This Calculator
- Enter wave frequency (Hz) and wavelength (m).
- Read wave speed (m/s) calculated from v = f * lambda.
- Review period (s), angular frequency (rad/s), and wave number (rad/m).
- Check Mach number to compare the wave speed against the speed of sound in air (343 m/s).
How the result changes with Frequency (Hz)
| Frequency (Hz) | Wave Speed (m/s) |
|---|---|
| 220 | 171.6 |
| 330 | 257.4 |
| 660 | 514.8 |
| 1,100 | 858 |
What each input means
- Frequency (Hz)
- Wave frequency in hertz (cycles per second).
- Wavelength (m)
- Distance between consecutive wave peaks.
What each result means
- Wave Speed (m/s)
- v = fλ.
- Period (s)
- T = 1/f. Time for one complete cycle.
- Angular Frequency (rad/s)
- ω = 2πf.
- Wave Number (rad/m)
- k = 2π/λ.
- Mach Number
- Speed relative to sound in air (343 m/s).
- Wave Speed (km/h)
- Speed in kilometers per hour.
- Wave Speed (mph)
- Speed in miles per hour.
How this is calculated
Worked example, using the default values
- Identify Input ParametersFrequency (Hz) = 440, Wavelength (m) = 0.78 = 2 input(s) provided
- Calculate Wave SpeedWave Speed = frequencyHz * wavelengthM343.2 = 343.2
- Calculate PeriodPeriod = 1 / frequencyHz0.00227 = 0.00227
- Calculate Angular FrequencyAngular Frequency = 2 * π * frequencyHz2764.6 = 2764.6
Engine last updated . Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the default input use 440 Hz and 0.78 m?
440 Hz is concert pitch A4, the reference tone orchestras tune to, chosen as a familiar example frequency. Paired with a wavelength of 0.78 m, v = fλ works out to roughly 343 m/s — the speed of sound in air at room temperature — so the default inputs represent a sound wave at that pitch traveling through ordinary air.
Can I use this calculator to find the speed of light or sound in a specific medium?
Not directly — the calculator only computes v = fλ from whatever frequency and wavelength you supply; it has no model of air temperature, water density, or optical medium built in. If you want the actual propagation speed of sound in a specific gas or light in a specific material, you'd need to look that value up (or derive it from the medium's own physics) and treat it as one of your inputs instead.
Why does the Mach number output use 343 m/s specifically?
343 m/s is the standard reference speed of sound in dry air at about 20°C (room temperature), and the calculator divides your computed wave speed by that fixed constant to get the Mach number. It's meant as an intuitive comparison, not a claim that your wave is actually sound moving through air at that exact temperature — the same math applies regardless of what kind of wave you entered.
If I double the frequency and keep wavelength the same, what happens to the other outputs?
Wave speed doubles directly since v = fλ is linear in frequency, and Mach number, km/h, and mph all scale with it. Period is the reciprocal of frequency, so it's cut in half, while angular frequency (ω = 2πf) doubles right along with the frequency you entered. Wave number, which depends only on wavelength, is unaffected.
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