Ideal String Tension and Frequency Calculator
Relate ideal vibrating-string tension, length, linear mass density and harmonic frequency.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the ideal stretched-string wave speed from tension and linear density. Apply fixed-end harmonic frequency n×speed/(2×length).
f_n=n/(2L)√(T/μ); T=μ(2Lf_n/n)²
Worked example
Length 0.65 m, linear density 5 g/m and fundamental 110 Hz imply wave speed 143 m/s and tension 102.245 N.
Assumptions and input details
Flexible uniform string with fixed ends, small transverse vibration and negligible stiffness. Harmonic number 1–100. Density is mass per length, not material volume density. No instrument setup, material breaking strength or safe load is inferred. The unit selector for the calculated quantity remains available.
References: OpenStax: stretched-string wave speed
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
SI prefixes are explicit: for example, milli means one thousandth, micro one millionth and kilo one thousand. Changing a unit changes the interpretation of the entered number.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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