PHYS 125 MK III

v = fλ

The wave speed equation; relates speed, frequency, and wavelength.

ω = 2πf

Angular frequency; how fast a wave oscillates in radians per second.

k = 2π/λ

Wave number; how fast a wave repeats in space (radians per meter).

y(x, t) = A sin(kx - ωt)

General wave equation for a traveling wave (A = amplitude).

φ (phi)

Phase constant; shifts a wave left or right in time or space.

ΔL = mλ

Constructive interference condition; path difference equals an integer multiple of wavelength.

ΔL = (m + ½)λ

Destructive interference condition; path difference equals a half-integer multiple of wavelength.

d sinθ = mλ

Double-slit interference bright fringe condition.

d sinθ = (m + ½)λ

Double-slit interference dark fringe condition.

y(x, t) = 2A cos(ω t) sin(k x)

Standing wave equation (result of two identical waves moving in opposite directions).

f_beat = |f₁ - f₂|

Beat frequency; rate of loud-soft alternation when two waves of close frequencies interfere.

y(x, t) = 2A cos(π(f₁ - f₂) t) sin(2π x f_avg t)

Equation describing beats from two close frequencies (f_avg = average frequency).

T = 1/f

Period of a wave; time for one full cycle.

E = hf

Photon energy; energy of a photon.

E = hc/λ

Photon energy expressed using wavelength.

K_max = hf - φ

Photoelectric effect; maximum kinetic energy of ejected electrons (φ = work function).

p = h/λ

Photon momentum / de Broglie relation for particles.

E_n = -13.6 eV / n²

Bohr model energy levels for hydrogen atom.

ΔE = Ehigh - Elow = hf

Energy of absorbed or emitted photon equals the difference between energy levels.

1/λ = R_H(1/n₁² - 1/n₂²)

Rydberg equation; relates wavelength to electron transitions in hydrogen.

R_H = 1.097×10⁷ m⁻¹

Rydberg constant.

h = 6.626×10⁻³⁴ J·s

Planck’s constant.

c = 3.00×10⁸ m/s

Speed of light.

I ∝ A²

Wave intensity is proportional to amplitude squared.

v = ω/k

Relationship between angular frequency and wave number for wave speed.

λ = h/p

De Broglie wavelength relation (particle wavelength).