Wavelength Calculator
Wavelength (represented by the Greek letter lambda, λ) is the distance between successive crests, troughs, or identical points of a wave. It's a fundamental property of all waves, including sound waves, light waves, water waves, and electromagnetic waves.
Wavelength determines many physical properties: the color of light (different wavelengths = different colors), the pitch of sound (shorter wavelength = higher pitch), and how waves interact with objects and other waves.
Key wavelength ranges in physics:
- Gamma rays: Less than 10 picometers (10⁻¹² m)
- X-rays: 10 pm to 10 nm
- Ultraviolet: 10 nm to 400 nm
- Visible light: 400 nm to 750 nm
- Infrared: 750 nm to 1 mm
- Microwaves: 1 mm to 1 m
- Radio waves: 1 m to 100 km
Enter frequency and wave speed to calculate wavelength instantly:
- Frequency (f): Number of wave cycles per second in Hertz
- Wave Speed (v): Speed at which wave propagates through medium
The calculator instantly provides:
- Wavelength in meters (m)
- Wavelength in centimeters (cm)
- Wavelength in nanometers (nm) - useful for light waves
- Wave type identification (light, sound, radio, etc.)
- Unit conversions between Hz, kHz, MHz, GHz and m/s, km/s
Here are typical wavelength values for common waves:
| Wave Type | Frequency | Speed | Wavelength | Application |
|---|---|---|---|---|
| AM Radio | 1 MHz | 3×10⁸ m/s | 300 m | Radio broadcasting |
| FM Radio | 100 MHz | 3×10⁸ m/s | 3 m | FM radio stations |
| Wi-Fi (2.4 GHz) | 2.4 GHz | 3×10⁸ m/s | 12.5 cm | Wireless networking |
| Middle C Sound | 261.6 Hz | 343 m/s | 1.31 m | Musical note |
| Red Light | 4.3×10¹⁴ Hz | 3×10⁸ m/s | 700 nm | Visible light |
| Ultrasound | 2 MHz | 1,480 m/s | 0.74 mm | Medical imaging |
Use the speed presets for common waves: Speed of light for electromagnetic waves, speed of sound in air/water for acoustic waves. Custom speed for specialized calculations.
Below are answers to frequently asked questions about wavelength calculations and applications:
For electromagnetic waves (light, radio, X-rays), always use speed of light (c = 299,792,458 m/s ≈ 3×10⁸ m/s):
λ = c / f
Where c = 3×10⁸ m/s (speed of light in vacuum)
For sound waves, you need to know the medium: air (343 m/s), water (1,480 m/s), steel (5,960 m/s). Temperature and pressure affect sound speed in air.
Wavelength changes when waves enter different materials because wave speed changes, even though frequency remains constant:
λmaterial = λvacuum / n
Where n = refractive index of material
Examples: Air: n≈1.0003, Water: n≈1.33, Glass: n≈1.5, Diamond: n≈2.42
Wavelength is critical in numerous technologies:
| Technology | Typical Wavelength | Application |
|---|---|---|
| Wi-Fi | 12.5 cm (2.4 GHz) | Wireless internet |
| Bluetooth | 12.5 cm (2.4 GHz) | Short-range communication |
| Microwave oven | 12.2 cm (2.45 GHz) | Heating food |
| GPS | 19 cm (1.575 GHz) | Navigation |
| Cell phones | 15-33 cm (900-1900 MHz) | Mobile communication |
| Fiber optics | 850, 1300, 1550 nm | Internet backbone |
Each technology uses specific wavelengths optimized for their purpose: longer wavelengths penetrate better, shorter wavelengths carry more data.
Color perception is directly related to wavelength:
- Violet: 380-450 nm (highest frequency, shortest wavelength)
- Blue: 450-495 nm
- Green: 495-570 nm
- Yellow: 570-590 nm
- Orange: 590-620 nm
- Red: 620-750 nm (lowest frequency, longest wavelength)
Our eyes contain cones sensitive to different wavelength ranges. Mixing different wavelengths creates all the colors we see.
For electromagnetic waves, energy is directly proportional to frequency and inversely proportional to wavelength:
E = h × f = h × c / λ
Where h = Planck's constant (6.626×10⁻³⁴ J·s)
Shorter wavelength = higher frequency = higher energy photons
This explains why gamma rays (very short λ) are highly penetrating and dangerous, while radio waves (long λ) are harmless.
Wavelength determines how waves interact with obstacles and each other:
- Diffraction: Waves bend around obstacles comparable to their wavelength
- Interference: Constructive/destructive interference depends on path difference in wavelengths
- Resolution limit: Can't resolve details smaller than wavelength (limits microscope/telescope resolution)
- Antenna size: Optimal antenna length = λ/2 or λ/4
- Penetration: Longer wavelengths penetrate materials better (why AM radio works in tunnels)