Revise: Vibration of Strings, Resonance
Stationary waves, vibrating strings, the resonance column and organ pipes, and the intensity of waves.
Nodes (zero displacement) and antinodes (max displacement) are fixed, spaced λ/2 apart.
0.3 m between adjacent nodes gives λ = 0.6 m.
Closed pipe: first resonance at L = λ/4 (node at closed end, antinode at open end).
512 Hz resonating at L = 0.16 m gives v ≈ 327.7 m/s.
Open pipe: fundamental at L = λ/2 (antinode at both ends) — an octave above a closed pipe of the same length.
A 1.2 m open pipe has a fundamental of ≈ 141.7 Hz.
I = P/A; intensity falls off as a wave's power spreads over a larger area.
0.5 W over 10 m² gives an intensity of 0.05 W/m².
f = (1/2L)√(T/μ): shorter, tighter, lighter strings vibrate at higher frequency.
Tightening a guitar string raises its pitch by increasing T.