Waves & Simple Harmonic Motion Formulas
A complete list of waves & simple harmonic motion formulas, covering wave speed, frequency, SHM, pendulums, the Doppler effect, and sound intensity.
16 formulas. Use the interactive searcher to solve for any variable and convert units.
Open the interactive searcher →Wave speed
v = f·λ
v velocitym/sf frequencyHzλ wavelengthm
Period & frequency
T = 1 / f
T periodsf frequencyHz
SHM displacement
x = A·cos(ω·t)
x displacementmA amplitudemω angular frequencyrad/st times
Pendulum period
T = 2π·√(L / g)
T periodsL lengthmg gravitational accelerationm/s²
SHM velocity
v = −A·ω·sin(ω·t)
v velocitym/sA amplitudemω angular frequencyrad/st times
SHM acceleration
a = −ω²·x
a accelerationm/s²ω angular frequencyrad/sx displacementm
SHM max velocity
v_max = A·ω
v_max maximum velocitym/sA amplitudemω angular frequencyrad/s
Mass-spring period
T = 2π·√(m / k)
T periodsm masskgk spring constantN/m
Angular frequency
ω = 2π·f
ω angular frequencyrad/sf frequencyHz
Wave equation (number)
k = 2π / λ
k wave numberrad/mλ wavelengthm
Doppler effect (sound)
f' = f·(v ± v_o)/(v ∓ v_s)
f' observed frequencyHzf source frequencyHzv wave velocitym/sv_o observer velocitym/sv_s source velocitym/s
Standing wave frequency
f_n = n·v / (2·L)
f_n harmonic frequencyHzn harmonic numberv velocitym/sL lengthm
Speed of wave on string
v = √(T / μ)
v velocitym/sT tensionNμ linear densitykg/m
Intensity
I = P / A
I intensityW/m²P powerWA aream²
Sound intensity level
β = 10·log(I / I₀)
β sound leveldBI intensityW/m²I₀ reference intensityW/m²
Beat frequency
f_beat = |f₁ − f₂|
f_beat beat frequencyHzf₁ frequencyHzf₂ frequencyHz