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# Superposition of waves with different frequencies.

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1. In a physics mock, we were given a question in which there were two waves. One had a larger amplitude and frequency that the other. We were told to draw the resulting wave and from that work out the frequency and wavelength of the wave which is the result of the superposing of the two given waves.

To help put across my point I have modeled the waves using transformed sine graphs.

The two given waves resembled the following:
https://www.dropbox.com/s/0y9v5o31q9...24.49.png?dl=0

Which resulted in the following:
https://www.dropbox.com/s/njdcpfr3sw...24.25.png?dl=0

Can someone please shed some light on this as the teacher avoided the question when asked about it and nobody had a clue. I researched and found something about beat frequency, but we weren't even told the correct answer so I couldn't tell if you were supposed to work out the beat frequency. Thanks for any help.
Attached Images

2. This seems likely to be a question about adding harmonically related sinewaves rather than beats.

beats is when you add very similar frequencies and get a much slower series of cancellations... like this

When you add sinewaves at harmonically related frequencies, you get a wave at the fundamental frequency that has a different shape from sine, if you add the correct harmonics at the correct amplitude you can produce square, triangle, sawtooth waveforms (or practically anything else you want). This is how early analogue synthesizers worked fwiw. You can probably see your resultant waveform is beginning to look a bit more like a square wave (or possibly triangle) and a few more harmonics at the correct amplitudes would really start to get it quite close...
e.g

fwiw The reverse process of taking a waveform and working out which sinewaves it can be made up of is called Fourier analysis & you'll probably run into it again if you do a STEM course at uni.

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