Wave Interference Calculator

Superpose two sinusoidal waves and report beat frequency, resultant amplitude, and representative waveform data.

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Save to create a persistent, shareable workspace.

What This Calculator Does

This calculator adds two sinusoidal waves with independent amplitudes, frequencies, and phases, then summarizes the resulting interference pattern. It reports both static quantities like phase offset and dynamic quantities like beat frequency and sample waveform points.

It combines Amplitude 1, Amplitude 2, Frequency 1, Frequency 2 to estimate Resultant Amplitude, Beat Frequency, Phase Difference.

Formula & Method

Core equations: The superposition is

y(t)=A_1\sin(2\pi f_1 t+\phi_1)+A_2\sin(2\pi f_2 t+\phi_2)

. For equal frequencies, the resultant amplitude is

A_r=\sqrt{A_1^2+A_2^2+2A_1A_2\cos(\Delta\phi)}

and the beat frequency magnitude is

f_b=|f_1-f_2|

Notation used in the formulas: $R$ = Resultant Amplitude; $x_{1}$ = Amplitude 1; $x_{2}$ = Amplitude 2; $x_{3}$ = Frequency 1; $x_{4}$ = Frequency 2; $x_{5}$ = Phase 1; $x_{6}$ = Phase 2.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you want to inspect whether two tones or signals reinforce or cancel, or when estimating the envelope modulation caused by two nearby frequencies.

Reference Book

University Physics with Modern Physics

Hugh D. Young and Roger A. Freedman · Pearson

A common undergraduate physics text covering mechanics, electricity, waves, energy, and introductory modern physics.

View Book

Inputs Used

Amplitude 1: Used directly in the calculation.
Amplitude 2: Used directly in the calculation.
Frequency 1: Used directly in the calculation.
Frequency 2: Used directly in the calculation.
Phase 1: Used directly in the calculation.
Phase 2: Used directly in the calculation.
Waveform Window: Used directly in the calculation.

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