Calculate frequency, wavelength, or wave speed using the wave equation v = f × λ. Enter any two known values to find the third.
| Quantity | Formula | Result |
|---|
| Medium | Speed |
|---|---|
| Sound in air (20°C) | 343 m/s |
| Sound in water | 1,481 m/s |
| Sound in steel | 5,960 m/s |
| Light in vacuum | 299,792,458 m/s |
| Light in water | ~225,000,000 m/s |
| Radio waves | 299,792,458 m/s |
The wave equation v = f × λ relates three fundamental properties of any wave — its speed (v), frequency (f), and wavelength (λ). It applies to all types of waves: sound waves, light waves, radio waves, water waves, and seismic waves. Knowing any two of the three values allows you to calculate the third instantly.
| Property | Symbol | Unit | Description |
|---|---|---|---|
| Frequency | f | Hertz (Hz) | Number of wave cycles per second |
| Wavelength | λ (lambda) | Meters (m) | Distance between two consecutive wave peaks |
| Wave Speed | v | m/s | Speed at which the wave travels through a medium |
| Period | T | Seconds (s) | Time for one complete wave cycle (T = 1/f) |
| Amplitude | A | varies | Maximum displacement from equilibrium (not in this equation) |
| Photon Energy | E | Joules (J) | Energy of a photon: E = hf (EM waves only) |
| Type | Frequency Range | Wavelength Range |
|---|---|---|
| Radio waves | < 300 MHz | > 1 m |
| Microwaves | 300 MHz – 300 GHz | 1 mm – 1 m |
| Infrared | 300 GHz – 400 THz | 750 nm – 1 mm |
| Visible light | 400 – 700 THz | 430 – 750 nm |
| Ultraviolet | 700 THz – 30 PHz | 10 – 430 nm |
| X-rays | 30 PHz – 30 EHz | 0.01 – 10 nm |
| Gamma rays | > 30 EHz | < 0.01 nm |
Frequency (f) is the number of complete wave cycles that pass a point per second, measured in Hertz (Hz). 1 Hz = 1 cycle per second. A sound wave at 440 Hz vibrates 440 times per second — that's the musical note A4 used to tune instruments.
Wavelength (λ) is the distance between two consecutive identical points on a wave — typically measured from peak to peak or trough to trough. Higher frequency waves have shorter wavelengths, and lower frequency waves have longer wavelengths. This inverse relationship is captured in the wave equation: λ = v ÷ f.
The speed of sound in dry air at 20°C is approximately 343 m/s (1,235 km/h or 767 mph). It's faster in warmer air, faster in water (~1,481 m/s), and much faster in steel (~5,960 m/s). Sound cannot travel through a vacuum because it requires a medium to propagate.
The speed of light in a vacuum (c) is exactly 299,792,458 m/s — approximately 3 × 10⁸ m/s or 300,000 km/s. All electromagnetic waves (radio, light, X-rays) travel at this speed in a vacuum. Light slows down when passing through a medium like glass or water.
The period (T) is the time it takes for one complete wave cycle to pass a point. It is the reciprocal of frequency: T = 1 ÷ f. A wave with a frequency of 50 Hz has a period of 1/50 = 0.02 seconds (20 milliseconds).
Planck's constant (h = 6.626 × 10⁻³⁴ J·s) relates the energy of a photon to its frequency: E = h × f. Higher frequency light (like UV or X-rays) carries more energy per photon than lower frequency light (like radio waves or infrared). This is why UV light can cause sunburn but radio waves cannot.
In a transverse wave, the medium oscillates perpendicular to the direction of wave travel — like light waves or waves on a string. In a longitudinal wave, the medium oscillates parallel to the direction of travel — like sound waves, which create compressions and rarefactions in air.