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Beat Frequency and Wave Interference Simulator

Two machines running at close speeds on the same foundation or frame produce a vibration that rises and falls periodically. This beat is why measured amplitude fluctuates and why the machines seem to "hum".

Speed equivalents: — / — rpm

Low frequencies may be inaudible; move the frequencies to 200–1000 Hz to hear the beat.

Beat frequency —
Beat period
—
Envelope maximum (A₁+A₂)
— mm/s
Envelope minimum |A₁−A₂|
— mm/s

Total signal and envelope

Components (first few revolutions)

These tools are intended for preliminary assessment and training. Decisions on critical equipment should be based on on-site measurement and expert evaluation.

How to use

  1. Enter the frequency (Hz) and amplitude of both sources; speed equivalents are shown below.

  2. Bring the frequencies closer and watch the beat period grow.

  3. From the period of the amplitude swing measured on site, find the frequency difference of the two sources.

Theory & formulas

x(t) = A1sin(2πf1t) + A2sin(2πf2t + φ).

Envelope: E(t) = √(A1² + A2² + 2A1A2cos(2π(f1−f2)t − φ)), swinging between A1+A2 and |A1−A2|.

Beat frequency fb = |f1 − f2|, period 1/fb. The spectrum has no line at the beat; it shows two lines, and resolution must be finer than fb to separate them.

Frequently asked questions

How do you balance a machine with a beat?

Because amplitude and phase keep changing, the sources must be separated first: stop the neighbouring machine, increase resolution or use a tachometer-referenced (synchronous) measurement. Then balance on the 1X value of the machine concerned.