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Waves & soundSchool & A-level

Fixed-string harmonic frequencies

fₙ = n/(2L) √(T/μ)

Gives allowed frequencies for a stretched string fixed at both ends.

Symbols, conditions & references

When this applies

Small transverse displacement, uniform flexible string, constant tension and fixed nodes at both ends.

fₙ
frequency of harmonic nHz
n
positive integer harmonic numberdimensionless
L
vibrating lengthm
T
string tensionN
μ
mass per unit lengthkg m⁻¹
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A growing reference from school fundamentals through undergraduate and selected advanced physics. No finite collection contains every specialised equation or theory; use topic and level filters, and always check assumptions.

Definitions use original wording, and each reference links to source material. Study labels are guides, not exam-board checklists. Worked check questions are educational examples, not an exam question bank.

Equations use SI quantities unless stated otherwise. Numerical values retain the units, precision and conditions of their source. Diagrams are explanatory models; their captions identify simplifications.

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