Wave Systems Formulae

Best use as flashcards

dsinθ = nλ

d = distance between adjacent slits (or grating lines), in meters (m)

θ = angle from the central axis to the bright fringe

n = which bright fringe you're looking at (n = 0 is the central max, n = 1 is the first bright fringe on either side, etc.)

λ = wavelength of the light (meters, m)

nλ = dx/L

• n = which bright fringe

• λ = wavelength of light (meters, m)

• d = distance between the slits (meters, m)

• x = distance from the central bright fringe to the nth bright fringe on the screen (meters, m)

• L = distance from the slits (or grating) to the screen (meters, m)

f′ = f(v_w​/v_s ±​ v_w​)​​

• f' — observed frequency — hertz (Hz)

• f — source (actual) frequency — hertz (Hz)

• v_w — speed of wave — meters/second (ms^-1)

• v_s — speed of the source — meters/second (ms^-1)

v = fλ

• v — wave speed — meters/second (ms^-1)

• f — frequency — hertz (Hz)

• λ — wavelength — meters (m)

f = 1/T​

• f — frequency — hertz (Hz)

• T — period (time for one full cycle) — seconds (s)

d = 1/Lines per unit length

• d — slit spacing — meters (m) (after converting)

• Input: lines per unit length — lines/mm or lines/cm

• Output: d, in whatever length unit you started with (then convert to meters)

f_beat ​= f₁ ​− f₂

• f_beat — beat frequency (rate at which loudness pulses) — hertz (Hz)

• f₁ — frequency of first wave — hertz (Hz)

• f₂ — frequency of second wave — hertz (Hz)