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.

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:

Colour	Wavelength range
Violet	380–450 nm
Blue	450–495 nm
Green	495–570 nm
Yellow	570–590 nm
Orange	590–620 nm
Red	620–750 nm

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, photon energy connects the wave and quantum descriptions:

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.