Waves transfer energy without transferring matter. Core relation: v = f λ. Standing waves form from interference. Doppler effect changes frequency due to relative motion. Beats occur from interference of slightly different frequencies.
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Basic, standing, sound, Doppler, interference, beats, EM
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| Quantity | Formula / Relation | Notes / Units |
|---|---|---|
| Wave speed | v = f λ | Core relation |
| Frequency | f = 1 / T | Hz (hertz) |
| Angular frequency | ω = 2π f | rad/s |
| Wave number | k = 2π / λ | rad/m |
| Traveling wave (right) | y = A sin(kx − ωt + φ₀) | Most common form |
| Speed on string | v = √(T / μ) | T = tension, μ = mass/length |
| Sound speed (gas) | v = √(γ R T / M) | γ = adiabatic index, M = molar mass |
| Standing wave (string) | λₙ = 2L / n, fₙ = n v / (2L) | n = 1,2,3... (fundamental & harmonics) |
| Resultant amplitude | A = √(A₁² + A₂² + 2 A₁ A₂ cos δ) | δ = phase difference |
| Beats frequency | f_beat = |f₁ − f₂| | Absolute difference |
| Doppler effect | f' = f (v ± v₀) / (v ± v_s) | + if toward, − if away |
| EM wave speed | c = 3 × 10⁸ m/s | Speed in vacuum |
About wave motion
Waves transfer energy without transferring matter. The fundamental relation is v = f λ, where v is wave speed, f is frequency, and λ is wavelength. Standing waves form when two waves of the same frequency interfere.
Standing waves
For a string fixed at both ends: λ_n = 2L/n and f_n = nv/(2L), where n = 1,2,3... (fundamental and harmonics). Closed pipes have only odd harmonics; open pipes have all harmonics.
Doppler effect and interference
The Doppler effect changes observed frequency due to relative motion: f' = f (v ± v_observer) / (v ± v_source). Beats occur when two waves of slightly different frequencies interfere: f_beat = |f₁ − f₂|.