Audio Math Question

I have a question: Assme I used my computer to make a 20Hz audio track and a 20kHz audio track (both having the same amplitude), I burn it to CD, and play it on my stereo.

How does the sound waves add together so you hear the 20Hz and the 20kHz at the exact same time (assuming I have seperate sub-woofer and a tweeter)?

If you took the average of 20 and 20,000, you'd get (rounding off) 10,000 and would get a combiation of the two numbers.

So how are both sounds reproduced at the same time?

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Take pencil and paper and draw a long wave one or two periods across the page. That represents the 20Hz sound.

Now consider the 20 Hz wave trace your reference and draw on top of that a fast mowing wave with several cycles within one of the 20Hz periods (1000 cycles to be in scale but to understand is enough to draw 10 or 20).

Now you have a fast (HI Freq, packed with many cycles) wave superimposed (on top) of the Low frequency wave.

Mathematically is the sum of two sinusoid at different frequencies.

When the amplifier reproduce this voltage and drives the loudspeaker, the loudspeaker cone follows the complex waveform vibrating very fast around a central position that also moves slowly.

The resulting sound is exactly the 2 frequencies 20Hz and 20kHz and you could hear them you could sense them separately.

A more interesting experiment is to superimpose, let'say a 1000Hz and a

1010Hz then the two sinewaves will add and reinforce each other for 1/20 of a second and then the 1010Hz will be 1/2 cycle ahead of the other and be out of phase and the 2 waves will tend to erase each other for another 1/20 of a second.

The result sounds like a near 1005Hz warbled at 20Hz


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