Physics - Waves
Physics - Waves covers simple harmonic motion, wave properties, superposition, standing waves, sound, and the Doppler effect. You need to link frequency, wavelength, speed, phase, and boundary conditions.
Core rules
- Wave equation: v = fλ; for a wave on a string v = √(T/μ).
- SHM: a = −ω²x, T = 2π/ω; energy exchanges between kinetic and potential.
- Standing waves on a string fixed at both ends: λ_n = 2L/n, f_n = nv/(2L).
- In a pipe open at both ends, all harmonics occur; closed at one end, only odd harmonics.
- Doppler: observed frequency rises when source and observer approach.
Worked example
A string of length 0.80 m is fixed at both ends and carries waves at 240 m/s. Find the fundamental frequency. For the fundamental, the string holds half a wavelength: L = λ/2, so λ = 2L = 1.60 m. Then f = v/λ = 240/1.60 = 150 Hz. The next harmonic is 300 Hz, because fixed-end strings have f_n = nf_1. This is why the harmonic number equals the number of half-wavelengths.
Traps
- Using λ = L for a string fixed at both ends; the fundamental has λ = 2L.
- Confusing nodes (zero displacement) with antinodes (maximum displacement).
- Applying even harmonics to a pipe closed at one end.
- Forgetting that wave speed is set by the medium, while frequency is set by the source.
- Mixing angular frequency ω with ordinary frequency f; remember ω = 2πf.