Wavelength, Frequency & Wave Velocity Calculator (v = λ·f)
The fundamental wave relationship is v = λ × f, where v is the speed of propagation, λ (lambda) is the wavelength, and f is the frequency. This applies to all wave types: sound, light, radio waves, microwaves, and more. Enter any two values and the calculator instantly solves for the third.
The wave equation is **v = λ · f**: wave speed (m/s) = wavelength (m) × frequency (Hz). To find wavelength: λ = v / f. To find frequency: f = v / λ. Example: a 440 Hz sound wave in air (343 m/s) has wavelength λ = 343 / 440 ≈ **0.78 m**. WiFi at 2.4 GHz has λ ≈ **12.5 cm**. Visible light at 550 nm oscillates at ≈ **545 THz**.
When to use this calculator
- Solve wave problems in physics and acoustics
- Calculate wavelengths of radio or WiFi signals
- Determine light frequency by color
- Understand the electromagnetic spectrum
- Calculate musical instrument frequencies
Example: Wavelength of WiFi 2.4 GHz
- Given: frequency f = 2.4 GHz = 2,400,000,000 Hz; speed of light c = 299,792,458 m/s.
- Formula: λ = v / f = 299,792,458 / 2,400,000,000.
- Result: λ ≈ 0.1249 m ≈ 12.5 cm.
- Interpretation: WiFi 2.4 GHz antennas are typically ~6 cm long — half the wavelength (λ/2 dipole antenna is the standard design for maximum efficiency).
How it works
2 min readThe Fundamental Wave Equation
The relationship v = λ · f connects speed, wavelength, and frequency for any wave — mechanical or electromagnetic. Rearranged for each unknown:
Sound Wavelengths in Air (343 m/s at 20°C)
| Frequency | Wavelength | Real-world example |
|---|---|---|
| 20 Hz | 17.15 m | Lower limit of human hearing |
| 100 Hz | 3.43 m | Bass drum / subwoofer |
| 440 Hz | 0.78 m | Musical note A4 (concert pitch) |
| 1,000 Hz | 34.3 cm | Mid-range human voice |
| 4,000 Hz | 8.6 cm | Speech consonants |
| 20,000 Hz | 1.7 cm | Upper limit of human hearing |
Radio & Light Wavelengths
| Type | Frequency | Wavelength |
|---|---|---|
| AM radio | 1 MHz | 300 m |
| FM radio | 100 MHz | 3 m |
| WiFi 2.4 GHz | 2,400 MHz | 12.5 cm |
| WiFi 5 GHz | 5,000 MHz | 6 cm |
| Microwave oven | 2,450 MHz | 12.2 cm |
| Red light | 700 nm | 428 THz |
| Green light | 550 nm | 545 THz |
| Violet light | 380 nm | 790 THz |
| UV (solar) | 300 nm | 1,000 THz |
Wave Propagation Speeds
| Medium | Speed |
|---|---|
| Sound in air (20°C) | 343 m/s |
| Sound in water | 1,480 m/s |
| Sound in steel | 5,960 m/s |
| Light in vacuum | 299,792,458 m/s |
| Light in fiber optic | ~200,000,000 m/s |
Key Tips & Common Mistakes
Frequently asked questions
What is the formula for wavelength?
Wavelength is calculated with λ = v / f, where v is the wave's propagation speed (in m/s) and f is the frequency (in Hz). The result is the wavelength in meters. Example: a 440 Hz sound wave in air (343 m/s) → λ = 343 / 440 ≈ 0.78 m (78 cm).
What is the wavelength of WiFi?
WiFi 2.4 GHz: λ ≈ 12.5 cm. WiFi 5 GHz: λ ≈ 6 cm. WiFi 6 GHz: λ ≈ 5 cm. Longer wavelengths (2.4 GHz) penetrate walls better; shorter wavelengths offer higher bandwidth but less range.
What is the wavelength of visible light?
Visible light ranges from 380 nm (violet) to 700 nm (red). Green light (~550 nm) oscillates at ≈ 545 THz. Ultraviolet is below 380 nm; infrared is above 700 nm.
What is the frequency of the musical note A4?
The standard A4 (concert pitch) is 440 Hz. In air at 20°C (343 m/s), its wavelength is λ = 343 / 440 ≈ 0.78 m (78 cm). In water (1,480 m/s), λ ≈ 3.36 m.
What's the difference between Hz, kHz, MHz, and GHz?
1 kHz = 1,000 Hz; 1 MHz = 1,000,000 Hz; 1 GHz = 1,000,000,000 Hz; 1 THz = 10¹² Hz. FM radio: ~88–108 MHz (λ ≈ 3 m). Microwave oven: 2.45 GHz (λ ≈ 12.2 cm). Visible light: 400–790 THz.
Is the speed of sound always 343 m/s?
No. 343 m/s is the speed in air at 20°C. It changes with medium: water ≈ 1,480 m/s, steel ≈ 5,960 m/s. In air, speed increases by roughly 0.6 m/s per degree Celsius. Speed changes affect wavelength but not frequency.
What is the electromagnetic spectrum?
The full range of EM radiation ordered by frequency: Radio (< 3 GHz) → Microwave (3–300 GHz) → Infrared (300 GHz–430 THz) → Visible light (430–790 THz) → Ultraviolet → X-rays → Gamma rays (> 10 EHz). Only visible light is detected by human eyes.
Why are subwoofers so large?
Low frequencies have very long wavelengths: at 20 Hz in air, λ ≈ 17 m; at 100 Hz, λ ≈ 3.4 m. A speaker cone must be large enough to displace sufficient air to reproduce these long wavelengths efficiently. High-frequency tweeters can be tiny because their wavelengths are just centimeters.
What happens to wavelength when a wave changes medium?
Frequency stays constant when a wave crosses a medium boundary, but the wave speed changes, so wavelength changes too. When light passes from vacuum into glass (speed ≈ 200,000 km/s), its frequency is unchanged but λ shrinks to about 67% of the vacuum value.