Beat Frequency and Envelope Calculator
Find beat rate, beat period and an equal-amplitude envelope from two tone frequencies.
YOUR CALCULATION
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
Take the absolute frequency difference as the rate of envelope maxima. Calculate the mean carrier frequency and show the absolute modulation envelope.
Beat rate=|f1−f2|; envelope=2|cos(π(f1−f2)t)|; beat period=1/|f1−f2|
Worked example
440 Hz and 442 Hz produce a 2 Hz beat rate, one envelope maximum every 0.5 s and four beat cycles in 2 s.
Assumptions and input details
Equal-amplitude sinusoids, zero initial phases and a linear sum. The envelope is a mathematical amplitude factor, not a loudness prediction. Audible beating is most meaningful for nearby frequencies; widely separated tones still have a difference frequency but may not sound like slow beats. Identical frequencies have a constant envelope. The display covers at most the first four beat cycles and does not render the high-frequency carrier or play sound.
References: OpenStax: wave interference and beats
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
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.
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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