Wave Frequency Calculator
This wave frequency calculator solves v = f × λ for any unknown — wave speed, frequency, or wavelength. Use the speed of light preset (3 × 10⁸ m/s) for electromagnetic waves or the speed of sound preset (343 m/s) for acoustic waves. Scientific notation input is supported.
Frequently Asked Questions
What is the wave frequency formula?
The wave equation is v = f × λ, where v is the wave speed in m/s, f is the frequency in Hz (cycles per second), and λ (lambda) is the wavelength in meters. Rearranging gives f = v/λ and λ = v/f.
What is the frequency of visible light?
Visible light has frequencies between about 430 THz (700 nm red) and 750 THz (400 nm violet). For example, green light at 550 nm has a frequency of 3×10⁸ / 550×10⁻⁹ ≈ 5.45 × 10¹⁴ Hz (545 THz).
What is the wavelength of 440 Hz (A4)?
Sound at 440 Hz in air (speed of sound ≈ 343 m/s) has a wavelength of 343/440 ≈ 0.780 meters (about 78 cm). In water where sound travels at ~1480 m/s, the same frequency has a wavelength of about 3.36 m.
What is the speed of light?
The speed of light in a vacuum is exactly 299,792,458 m/s, commonly approximated as 3 × 10⁸ m/s or 300,000 km/s. Light travels slightly slower through other media (glass, water), which is why lenses can focus it.
How does frequency relate to energy?
For photons (light particles), energy E = h × f, where h = 6.626 × 10⁻³⁴ J·s is Planck's constant. Higher-frequency light (UV, X-rays) carries more energy per photon than lower-frequency light (infrared, radio). This is why UV causes sunburn but visible light does not.
What is the wavelength of a 2.4 GHz Wi-Fi signal?
A 2.4 GHz Wi-Fi signal: λ = c/f = 3×10⁸ / 2.4×10⁹ ≈ 0.125 meters (12.5 cm). The 5 GHz Wi-Fi band has wavelength ≈ 6 cm. Shorter wavelengths carry more data but are absorbed more easily by walls and obstacles.
Why do AM radio waves travel farther than FM waves?
AM radio (535–1705 kHz, λ ≈ 175 m – 560 m) has much longer wavelengths than FM radio (87.5–108 MHz, λ ≈ 2.8–3.4 m). Longer wavelengths diffract around obstacles and follow Earth's curvature better, allowing AM stations to broadcast over thousands of kilometers.
How do I convert nanometers to frequency?
To convert wavelength in nanometers to frequency: f = c/λ = 3×10⁸ / (λ_nm × 10⁻⁹). Example: 500 nm green light → f = 3×10⁸ / (500×10⁻⁹) = 6 × 10¹⁴ Hz = 600 THz. Use this calculator by entering the speed of light and wavelength in meters (500 nm = 5×10⁻⁷ m).
The Wave Equation
All waves — light, sound, radio, water — obey a simple relationship between their speed, frequency, and wavelength.
v = f × λ
- v — wave speed (m/s)
- f — frequency (Hz = cycles per second)
- λ (lambda) — wavelength (m)
Common Wave Speeds
| Medium | Speed (m/s) |
|---|---|
| Light in vacuum (c) | 3.00 × 10⁸ |
| Sound in air (20°C) | 343 |
| Sound in water | 1,480 |
| Sound in steel | 5,120 |
Electromagnetic Spectrum
| Type | Wavelength | Frequency |
|---|---|---|
| Radio | > 1 m | < 300 MHz |
| Microwave | 1 mm – 1 m | 300 MHz – 300 GHz |
| Infrared | 700 nm – 1 mm | 300 GHz – 430 THz |
| Visible light | 400 – 700 nm | 430 – 750 THz |
| Ultraviolet | 10 – 400 nm | 750 THz – 30 PHz |
| X-ray | 0.01 – 10 nm | 30 PHz – 30 EHz |
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