Wavelength ↔ Frequency Calculator - EM & Sound Waves

Wave equation

v = λ × f - wave speed equals wavelength times frequency. For EM waves in a vacuum, v = c ≈ 2.998 × 10⁸ m/s. For sound in air at 20°C, v ≈ 343 m/s.

This relationship describes both electromagnetic and mechanical waves, but the speed depends on the wave and its medium. The calculator uses the selected speed to solve the relationship; it does not treat sound or a custom-speed wave as light.

EM spectrum regions

• Gamma ray: <0.01 nm
• X-ray: 0.01–10 nm
• Ultraviolet: 10–400 nm
• Visible light: 400–700 nm
• Infrared: 700 nm–1 mm
• Microwave: 1 mm–10 cm
• Radio wave: >10 cm

Sound wave context

Unlike electromagnetic waves, sound waves are longitudinal mechanical waves that require a medium. In air at 20°C, sound travels at approximately 343 m/s. Using the wave equation:

• Concert A pitch (440 Hz): λ = 343 / 440 ≈ 0.78 m
• Bass guitar low E (41 Hz): λ ≈ 8.4 m
• Ultrasound imaging (2 MHz): λ ≈ 0.17 mm in soft tissue (speed ~1,540 m/s)

Sound travels faster in denser media: ~1,480 m/s in water and ~5,120 m/s in steel.

Visible light and colour

Within the visible band (approximately 380–750 nm), wavelength determines perceived colour:

Sunsets appear red/orange because shorter wavelengths (violet, blue) scatter more strongly in the atmosphere (Rayleigh scattering), leaving longer wavelengths to dominate at low solar angles.

Photon energy connection

For electromagnetic radiation only, photon energy connects the wave and quantum descriptions. The result panel shows this value in Light / EM mode and intentionally omits it for sound and custom waves: mechanical waves are not photons, even though they also have a wavelength and frequency.

E = h×f = h×c / λ

Where h = 6.626 × 10⁻³⁴ J·s (Planck’s constant). A 500 nm (green) photon carries approximately 2.5 eV of energy. This formula bridges classical wave physics and quantum mechanics, explaining why UV light causes sunburn (high energy) while radio waves do not.