ScienceApril 12, 2026

Wavelength Calculator Guide: Wavelength and Frequency Relationship (2026)

Q: What is the wave equation?

The wave equation relates wavelength (λ), frequency (f), and wave speed (v): v = λ × f, or equivalently λ = v/f. For electromagnetic waves in vacuum, v = c = 3 × 10⁸ m/s. For sound in air at 20°C, v ≈ 343 m/s. This equation applies to all types of waves — light, sound, water, and radio.

Q: What is the wavelength of visible light?

Visible light spans wavelengths from about 380 nm (violet) to 700 nm (red). Blue light is around 450-490 nm, green is 495-570 nm, yellow is 570-590 nm, and orange is 590-620 nm. Ultraviolet light has shorter wavelengths (10-380 nm) and infrared has longer wavelengths (700 nm to 1 mm).

Q: How do you convert between wavelength and frequency?

Use λ = v/f or f = v/λ. For electromagnetic waves: λ = (3 × 10⁸ m/s) / f. Example: FM radio at 100 MHz → λ = 3×10⁸ / 100×10⁶ = 3 meters. For sound: λ = 343 m/s / f. Concert A (440 Hz) → λ = 343/440 = 0.78 meters. Higher frequency always means shorter wavelength for a given medium.

Q: Why does wavelength change in different media?

When a wave enters a different medium, its speed changes but its frequency stays the same. Since v = λf and f is constant, wavelength must change proportionally with speed. Light slows in glass (to about 2 × 10⁸ m/s), so its wavelength shortens by a factor of 1.5 (the refractive index). This wavelength change is what causes refraction — the bending of light at material boundaries.

Q: What is the de Broglie wavelength?

The de Broglie wavelength describes the wave-like behavior of matter particles: λ = h/p = h/(mv), where h is Planck's constant (6.626 × 10⁻³⁴ J·s), m is mass, and v is velocity. An electron at typical speeds has a wavelength around 1 nanometer — small enough to diffract through crystal lattices. This wave-particle duality is fundamental to quantum mechanics.

By The hakaru Team·Last updated March 2026

Quick Answer

*Wave equation: v = λ × f (speed = wavelength × frequency).
*Light speed in vacuum: c = 3 × 10&sup8; m/s. Sound in air: 343 m/s.
*Visible light: 380 nm (violet) to 700 nm (red).
*Higher frequency = shorter wavelength for a given medium.

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The Wave Equation

v = λ × f

Three variables, three rearrangements: λ = v/f, f = v/λ, v = λf. This universal relationship applies to every type of wave — electromagnetic (light, radio, X-rays), mechanical (sound, water, seismic), and even quantum matter waves.

Electromagnetic Spectrum

Type	Wavelength Range	Frequency Range	Common Use
Radio	1 mm – 100 km	3 kHz – 300 GHz	Broadcasting, WiFi
Microwave	1 mm – 1 m	300 MHz – 300 GHz	Cooking, 5G, radar
Infrared	700 nm – 1 mm	300 GHz – 430 THz	Remote controls, thermal
Visible	380 – 700 nm	430 – 790 THz	Human vision
Ultraviolet	10 – 380 nm	790 THz – 30 PHz	Sterilization, tanning
X-ray	0.01 – 10 nm	30 PHz – 30 EHz	Medical imaging
Gamma	<0.01 nm	>30 EHz	Cancer treatment, astronomy

Sound Wave Wavelengths

Sound travels at about 343 m/s in air at 20°C. Human hearing spans 20 Hz to 20,000 Hz:

Lowest audible (20 Hz): λ = 343/20 = 17.15 meters
Concert A (440 Hz): λ = 343/440 = 0.78 meters
Highest audible (20 kHz): λ = 343/20,000 = 0.017 meters (1.7 cm)

This is why bass notes wrap around obstacles (long wavelength = more diffraction) while high-frequency sounds are easily blocked.

Wavelength in Different Media

When a wave enters a new medium, frequency stays constant but speed changes, so wavelength must change too. Light entering glass (refractive index n = 1.5) slows from 3 × 10&sup8; to 2 × 10&sup8; m/s. Its wavelength shortens by a factor of 1.5. This change in wavelength is what causes refraction — the bending of light at boundaries.

Practical Examples

WiFi (2.4 GHz): λ = 3×10&sup8; / 2.4×10&sup9; = 12.5 cm
FM Radio (100 MHz): λ = 3×10&sup8; / 10&sup8; = 3 meters
5G mmWave (28 GHz): λ = 3×10&sup8; / 2.8×10¹&sup0; = 10.7 mm
Green laser (532 nm): f = 3×10&sup8; / 532×10⁻&sup9; = 5.64 × 10¹&sup4; Hz

Convert between wavelength and frequency

Try the Free Wavelength Calculator →

Frequently Asked Questions

What is the wave equation?

v = λ × f. For light in vacuum, v = 3 × 10&sup8; m/s. For sound in air, v ≈ 343 m/s. It applies to all wave types.

What is the wavelength of visible light?

380 nm (violet) to 700 nm (red). Blue ≈ 450–490 nm, green ≈ 495–570 nm, yellow ≈ 570–590 nm.

How do you convert between wavelength and frequency?

λ = v/f. FM radio at 100 MHz: λ = 3 meters. Sound at 440 Hz: λ = 0.78 meters. Higher frequency = shorter wavelength.

Why does wavelength change in different media?

Frequency stays constant when entering a new medium, but speed changes. Since v = λf, wavelength changes proportionally. This causes refraction.

What is the de Broglie wavelength?

λ = h/(mv). Matter particles behave as waves. An electron's wavelength (~1 nm) is small enough to diffract through crystals, which is fundamental to quantum mechanics.