Mathematics · Advanced university
Angular frequency of a wave-equation mode · formula reference
For a string with fixed endpoints, length L, wave speed c, and positive integer mode n.
Formula
For a string with fixed endpoints, length L, wave speed c, and positive integer mode n.
ωₙ = cnπ/L
Worked example
A fixed-end string of length 12 m has wave speed 2 m/s. Write the angular frequency of mode n=10 as aπ rad/s. Find a. Round the final result to 4 decimal places if needed.
The wavenumber is nπ/L. Multiply by c = 2, giving (20/12)π rad/s.
1.6667
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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