Wavelength Calculator

The wave equation λ = v/f relates three fundamental wave properties: wavelength (λ, the distance between wave peaks), velocity (v, how fast the wave travels), and frequency (f, how many waves pass per second). This applies to all waves - electromagnetic, sound, water, and more. For electromagnetic waves in a vacuum, v = c = 3×10⁸ m/s.

The electromagnetic spectrum ranges from long-wavelength radio waves (λ > 1 m) to short-wavelength gamma rays (λ < 10⁻¹² m). In order of decreasing wavelength: radio, microwave, infrared, visible light (380-700 nm), ultraviolet, X-rays, gamma rays. All travel at c in vacuum but have vastly different energies (E = hc/λ).

Sound wavelength depends on frequency and medium. In air at 20°C (v = 343 m/s): a 440 Hz note (A4) has λ = 0.78 m, while 20 Hz bass has λ = 17 m. Sound travels faster in solids (steel: 5000 m/s) and liquids (water: 1480 m/s), giving longer wavelengths at the same frequency.

Louis de Broglie proposed that particles have wave properties with wavelength λ = h/(mv), where h is Planck's constant (6.626×10⁻³⁴ J·s), m is mass, and v is velocity. An electron at 1% of light speed has λ ≈ 2.4×10⁻¹° m. This wave nature explains electron diffraction and is fundamental to quantum mechanics.

Photon energy E = hf = hc/λ, where h = 6.626×10⁻³⁴ J·s and c = 3×10⁸ m/s. In electron volts: E(eV) = 1240/λ(nm). For example, green light (550 nm) has E = 1240/550 = 2.25 eV. Shorter wavelengths mean higher energy - UV and X-rays are more energetic than visible light.

Visible light wavelengths range from ~380 nm (violet) to ~700 nm (red). Our eyes detect these different wavelengths as colors. Blue light (~450 nm) has higher frequency and energy than red light (~650 nm). This is why UV light (shorter than violet) can cause sunburn - it carries more energy per photon.

Sound velocity in air increases with temperature: v ≈ 331 + 0.6T m/s, where T is temperature in Celsius. At 0°C, v = 331 m/s; at 20°C, v = 343 m/s; at 30°C, v = 349 m/s. Higher temperature means faster-moving air molecules, which transmit sound more quickly. This affects wavelength at constant frequency.

Wavelength and frequency are inversely proportional: when one doubles, the other halves (for constant velocity). From λ = v/f: high-frequency waves have short wavelengths, low-frequency waves have long wavelengths. A 1 MHz radio wave (long λ) vs a 1 GHz microwave (1000× shorter λ) illustrates this.