Part of JWAVE-02 — Waves: Standing Waves, Beats & Doppler Effect

Resonance and Musical Instruments

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Resonance occurs when a driving frequency matches a natural frequency of the system. In organ pipes, air columns resonate at specific frequencies determined by the pipe length and boundary conditions. In stringed instruments, the string vibrates at its natural frequencies when plucked or bowed. The frequency heard is primarily the fundamental, with overtones determining the timbre.

The pitch of a note corresponds to its fundamental frequency: higher pitch = higher f1f_1. Loudness corresponds to amplitude (intensity A2\propto A^2). Quality (timbre) depends on the overtone spectrum — the same note played on a flute (nearly sinusoidal, few overtones) sounds different from a violin (rich overtone content).

Key exam connections: (1) String vibrating in nn loops = nnth harmonic. (2) Open pipe produces both even and odd harmonics, giving richer sound. (3) Closed pipe produces only odd harmonics, giving a "hollow" sound. (4) Kundt's tube measures sound speed in solids: dust piles at nodes, separated by λ/2\lambda/2. (5) Temperature affects pipe resonance through sound speed: fTf \propto \sqrt{T}, so heating a pipe raises its pitch.

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