Wave Frequency Calculator
Solve for wave speed, frequency, or wavelength using the wave equation v = f × λ. You can also calculate the period (T = 1/f) from any frequency result.
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About the Wave Equation
All waves — sound, light, water, seismic, radio — share the same fundamental relationship:
v = f × λ
- v — wave speed, measured in metres per second (m/s)
- f — frequency, the number of complete wave cycles per second (Hz)
- λ (lambda) — wavelength, the physical distance between two consecutive crests (m)
Rearranging gives the other two forms:
- f = v / λ — frequency from speed and wavelength
- λ = v / f — wavelength from speed and frequency
The period T = 1 / f is the time for one complete wave cycle (measured in seconds). It is the reciprocal of frequency.
Wave Speed Reference Values
| Wave type | Medium | Approx. speed |
|---|---|---|
| Sound | Air (20 °C) | 343 m/s |
| Sound | Water | ~1,480 m/s |
| Sound | Steel | ~5,100 m/s |
| Light / EM waves | Vacuum | ~3 × 10⁸ m/s (c) |
| Seismic P-waves | Earth's crust | 5,000–8,000 m/s |
How to Use This Calculator
- Select which variable you want to solve for using the tabs at the top.
- Enter values for the other two variables in their respective fields.
- Choose appropriate units for each input using the dropdowns.
- Click Calculate — or try one of the quick example buttons to pre-fill common scenarios.
Results are automatically shown in SI units and include the wave period. For chemistry-related wave calculations, see the Molar Mass Calculator and the Ideal Gas Law Calculator.
Electromagnetic Spectrum
Electromagnetic waves travel at the speed of light (c ≈ 2.998 × 10⁸ m/s in a vacuum). Different regions of the EM spectrum are distinguished by frequency (or equivalently, wavelength):
| Region | Wavelength range | Frequency range |
|---|---|---|
| Radio waves | > 1 mm | < 300 GHz |
| Microwaves | 1 mm – 1 m | 300 MHz – 300 GHz |
| Infrared | 700 nm – 1 mm | 300 GHz – 430 THz |
| Visible light | 380–700 nm | 430–770 THz |
| Ultraviolet | 10–380 nm | 770 THz – 30 PHz |
| X-rays | 0.01–10 nm | 30 PHz – 30 EHz |
| Gamma rays | < 0.01 nm | > 30 EHz |
Frequently Asked Questions
What is the relationship between frequency and wavelength?
Frequency and wavelength are inversely proportional when wave speed is constant. If frequency doubles, the wavelength halves — the product f × λ always equals the wave speed. This is why high-frequency radio waves (like FM at ~100 MHz) have much shorter wavelengths than low-frequency AM waves (~1 MHz).
What is wave period and how does it relate to frequency?
Period (T) is the time — in seconds — it takes for one complete wave cycle to pass a fixed point. It is simply the reciprocal of frequency: T = 1/f. A wave at 440 Hz has a period of about 2.27 milliseconds.
Does the wave equation apply to light?
Yes. Electromagnetic waves including light obey v = fλ. In a vacuum the speed is c ≈ 2.998 × 10⁸ m/s. Green visible light at about 550 nm has a frequency of roughly 545 THz.
Why does sound travel faster in water than in air?
Sound is a mechanical wave; its speed depends on the elasticity and density of the medium. Water is much less compressible (more elastic) than air, so pressure disturbances travel faster despite water's higher density. The net effect is that sound travels roughly 4–5× faster in water (~1,480 m/s) than in air (~343 m/s).
What units should I use for wavelength?
It depends on the type of wave. Sound wavelengths are typically in centimetres or metres; radio and microwave wavelengths in metres to millimetres; visible light wavelengths in nanometres (nm); and X-ray wavelengths in picometres. This calculator supports all those unit choices via the dropdown.
