PHYS 125

Wave speed equation

v = fλ — speed of a wave equals frequency × wavelength

Frequency

f — number of wave cycles per second (Hz)

Period

T = 1/f — time for one full wave cycle

Angular frequency

ω = 2πf — measures how fast the wave oscillates in time (radians per second)

Wave number

k = 2π/λ — measures how fast the wave oscillates in space (radians per meter)

Amplitude (A)

Maximum displacement of the wave; related to energy or intensity

Wave equation

y(x,t) = A sin(kx - ωt + φ) — describes a traveling wave in space and time

Phase constant (φ)

Sets the starting point of the wave; usually 0 unless shifted

Constructive interference

Occurs when path difference ΔL = mλ (waves add together)

Destructive interference

Occurs when path difference ΔL = (m + ½)λ (waves cancel)

Double-slit interference

d sinθ = mλ — bright fringes occur when waves interfere constructively

Single-slit diffraction

a sinθ = mλ — dark fringes occur when light spreads through an opening

Superposition principle

y_total = y₁ + y₂ — total displacement is the sum of individual waves

Standing wave equation

y(x,t) = 2A cos(ωt) sin(kx) — result of two identical waves moving in opposite directions

Beat frequency equation

y(x,t) = 2A cos(π(f₁ - f₂)t) sin(2π x f_avg t) — describes beats from two close frequencies

Beats

f_beat = |f₁ - f₂| — difference between two close frequencies

Beat period

Tbeat = 1/fbeat — time between two beat pulses

Photon energy

E = hf = hc/λ — energy of a photon

Planck’s constant

h = 6.626×10⁻³⁴ J·s — fundamental constant for quantum effects

Speed of light

c = 3.00×10⁸ m/s

Photon momentum

p = h/λ — momentum carried by a photon

Photoelectric effect equation

K_max = hf - φ — max kinetic energy of ejected electron

Work function (φ)

Minimum energy needed to eject an electron from a material

Emission condition

Electrons are ejected only if hf > φ

Bohr energy levels

Eₙ = -13.6 eV / n² — quantized energy levels of hydrogen

Energy transition

ΔE = Ef - Ei = hf — photon absorbed/emitted when electron changes level

Rydberg equation

1/λ = R_H(1/n₁² - 1/n₂²) — relates wavelength to electron transitions

Rydberg constant

R_H = 1.097×10⁷ m⁻¹

Ionization wavelength (H)

λ < 365 nm — light shorter than this can ionize hydrogen (n=2)

Blackbody radiation

E = hf — energy emitted in discrete packets (photons)

Absorption process

Electron jumps to higher energy level; photon absorbed

Emission process

Electron drops to lower level; photon emitted

Amplitude definition

Max displacement; higher A → more energy

Wavelength (λ)

Distance between two identical points on consecutive waves

Frequency (f)

Number of waves passing a point each second

Period (T)

Time for one wave to pass a point (1/f)

Phase (φ)

Describes where in its cycle the wave starts

Path difference (ΔL)

Difference in distance traveled by two waves; determines interference type

Beats definition

Alternating loud/soft sound from two close frequencies

Diffraction

Bending/spreading of waves through narrow openings or edges

Interference

When two or more waves overlap and combine

Photoelectric effect

Light knocks electrons off metal only if photon energy exceeds work function

Bohr model

Electrons occupy discrete energy levels (quantized orbits)

Photon

Particle of light carrying energy E = hf