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Physics · 术语表

什么是 Spectrum and timbre？

又称： spectrum · timbre

Definition 21.14 High School Physics · 第 21 章 — Sound and Acoustics

The spectrum of a sound is the bar chart of its harmonics: one bar per $f_n$ , the height that harmonic’s strength. The ear hears $f_1$ as the pitch and the mix of strengths as the timbre — the sound’s color: instruments playing the same note share $f_1$ , differing only in their spectra.

The same A (220\, Hz): waveforms (top), spectra (bottom) — same fundamental and pitch; the violin’s harmonic ladder is its timbre. — The same A ( $220\,\mathrm{Hz}$ ): waveforms (top), spectra (bottom) — same fundamental and pitch; the violin’s harmonic ladder is its timbre.

示例

Example 21.15 (Why you recognize the caller)

A flute’s A is nearly a pure tone; a violin bowing the same $220\,\mathrm{Hz}$ adds strong harmonics at $440\,\mathrm{Hz}\text{, }660\,\mathrm{Hz}\text{ and }880\,\mathrm{Hz}$ . Same pitch and loudness, yet no one confuses them: a voice, too, is a spectrum you know by heart.

Example 21.19 (A violin’s A string)

A violin’s A string has $L = 32.8\,\mathrm{cm}$ and sounds $f_1 = 440\,\mathrm{Hz}$ : waves run along it at $v = 2Lf_1 = 2 \times 0.328 \times 440 \approx 289\,\mathrm{m}/\mathrm{s}$ — set by tension and mass, tuned by the peg. Pressing a finger shortens $L$ and raises every $f_n$ at once: the spectrum slides up.

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