String Harmonics (Both Ends Fixed) (νₙ = nv/(2L) = (n/2L)√(T/μ), n = 1, 2, 3, further terms)
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νₙ = nv/(2L) = (n/2L)√(T/μ), n = 1, 2, 3, ...
What each symbol means
| Symbol | What it stands for |
|---|---|
| L | Length of string (m) |
| T | Tension in string (N) |
| n | Harmonic number (positive integer) |
| v | Wave speed on string (m/s) |
| μ | Linear mass density (kg/m) |
| νₙ | Frequency of nth harmonic (Hz) |
When to use this
Both ends are nodes. Fundamental (n=1): ν₁ = v/(2L), string has 1 antinode. Wavelength: λₙ = 2L/n. All harmonics present (odd + even). String divides into n equal segments. Frequency ratios are 1:2:3:4:... NCERT Eq. 14.42.