Understanding Two Sine Wave Addition
Adding two sine waves is common in physics, music, electronics, vibration testing, and signal analysis. Each wave has amplitude, frequency, phase, and sometimes an offset. When two waves meet, their values add at every instant. The result can look stronger, weaker, shifted, or beating, depending on the input settings.
Same Frequency Case
When both waves share the same frequency, the sum becomes one new sine wave plus the combined offset. The new amplitude depends on the phase gap. In-phase waves reinforce each other. Opposite-phase waves cancel partly or fully. A ninety degree phase gap creates a result that is between those extremes. This calculator uses phasor addition for that case, so the final amplitude and phase are direct and stable.
Different Frequency Case
When frequencies differ, the sum is not one simple sine wave. It is a compound waveform. If the frequencies are close, the signal may rise and fall in loudness or strength. This pattern is called beating. The beat frequency equals the absolute difference between the two frequencies. The average frequency shows the rough carrier motion. The sample table helps you inspect this time behavior.
Why Phase Matters
Phase tells where a wave starts within its cycle. A phase of zero starts at the reference sine point. Positive phase moves the wave forward. Negative phase delays it. Small phase changes can strongly affect the sum, especially when amplitudes are similar. That is why this tool accepts degrees or radians and reports a wrapped phase value.
Practical Uses
Audio engineers use sine addition to study interference and stereo phase. Electrical learners use it for alternating signals. Mechanical teams use it for vibration combination. Students use it to check trigonometry identities. The calculator also supports offsets, so it can model signals riding above or below zero.
Reading the Results
First, review the instant values at the chosen time. Then check whether the inputs have the same frequency. Use the phasor result only for equal frequencies. Use the beat and sample data for unequal frequencies. Export the CSV for spreadsheets. Save the PDF when you need a compact record.
These exports make reviews easier and keep repeated experiments organized for later comparison across projects with teammates.