Wave Superposition
Add waves to see interference and beats
About this calculator
The Wave Superposition Calculator adds two sinusoids y = A·sin(2πft + φ) and reports what the sum looks like. With equal frequencies it performs phasor addition and classifies the interference as constructive, destructive, or partial, giving the resultant amplitude and phase; with different frequencies it switches to beats mode and reports the beat frequency |f₁ − f₂|, the beat period, and the carrier frequency, along with the envelope maximum A₁ + A₂ and minimum |A₁ − A₂|.
How to use the Wave Superposition calculator
- Enter the quantities you know, using the units shown on each field.
- Read the computed results — they update instantly as you type.
- Use the visual explanation to see how the quantities relate.
- Copy the page URL to share the exact calculation.
Common examples
- Two 5 Hz waves, A = 1 each, in phase → constructive: resultant amplitude 2
- Same waves 180° apart → destructive: the sum cancels to zero amplitude
- A₁ = 3, A₂ = 4 at 10 Hz, Δφ = 90° → partial interference, resultant amplitude 5, phase ≈ 53.13°
- 440 Hz + 444 Hz tones → beats: beat frequency 4 Hz, beat period 0.25 s, carrier 442 Hz
Frequently asked questions
How does the Wave Superposition calculator work?
Enter the known quantities and the calculator applies the governing physical law or scientific formula to find the unknowns, stating the equation it used and the units of every result. Computations run at high precision.
When would I use the Wave Superposition calculator?
It suits physics and chemistry homework, lab work, engineering estimates, and any time you want to explore how changing one quantity affects the others in a well-defined scientific relationship.
How accurate are the results?
The formula itself is evaluated at 30 significant digits of precision. Keep in mind that idealized models — such as neglecting friction, air resistance or measurement error — bound the real-world accuracy more than the arithmetic does.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.