# Combining Sine Waves on Chart

I would like to combine multiple sine waves with differing amplitudes, frequencies and phases into a single curve that I can display as a graph. What formula will I need to create the points for the curve?

-
Depends by what you mean by combine. A linear combination is one possibility: $y(t) = A_1 \cos(\omega_1 t + \phi_1) + A_2 \cos(\omega_2 t + \phi_2) + \ldots$ – Sasha Aug 12 '11 at 15:20
A bit of background on the project may be useful: I am working with raw hydrographical data and would like to chart tidal heights over time (e.g. a month). There is a sine wave for each influencing factor (e.g. lunar position, solar position) with their own amplitudes, durations and weights which I would like to aggregate into a single tidal curve. – Mike Aug 12 '11 at 15:36
Are you hoping to find a simple formula for your final curve? – Unreasonable Sin Aug 12 '11 at 15:45
Ideally, yes. I will then be able plot the results on a graph. – Mike Aug 12 '11 at 16:34

## 1 Answer

You can start out with just

$a_0 \sin(2\pi f_0 t + \phi_0 ) + a_1 \sin(2\pi f_1 t + \phi_1) + \cdots.$

If there are an infinite number of terms, then they might converge into a recognizable waveform that has an easy description as a function such as a square wave or a triangle wave.

-
Thanks for the reply. The resulting curve would not be a square wave or triangle wave. The resulting curve would be one which oscillates more on some occasions than others. – Mike Aug 12 '11 at 15:28