What is Standing wave? — Physics

Definition 21.16 High School Physics · Chapter 21 — Sound and Acoustics

A wave confined between the fixed ends of a string can settle into a standing wave: an oscillation in place, motionless points — nodes — alternating with points of maximal swing — antinodes. Nothing travels any more; the string vibrates in a fixed pattern.

The first three modes of a string fixed at both ends: n half-wavelengths fit in L, so _n = 2L/n and f_n = nf_1. — The first three modes of a string fixed at both ends: $n$ half-wavelengths fit in $L$ , so $\lambda_n = 2L/n$ and $f_n = nf_1$ .

Examples

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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Examples

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