[sdiy] Yet another try at explaining beat tones, etc.

[Aaron Lanterman]

On Jun 4, 2009, at 12:22 PM, Jerry Gray-Eskue wrote:

> Since the two frequencies are causing physical motion we can get  
> reinforcement of the (a-b)/2 as the physical motions interact. So do  
> we create the Beat signal here, or are the physics of the mechanical  
> motion preserving the two frequencies intact?

Well - the beat signal, say when you're tuning a guitar, is never  
really being created. You will not see it on any spectrum analyzer.  
You're perceiving say a 0.5 Hz amplitude modulation (since your ear  
can't tell the difference between the positive and negative parts of  
the wave), but there's no place anywhere that a 1 Hz signal actually  
exists.

In our Intro to Signal Processing class, in lab have students add two  
sine waves together of close frequencies and then look at their  
spectrogram in MATLAB, which gives a 2-D time-frequency plot of the  
content. In the spectrogram you have to pick a window size. Small  
windows give you high time resolution but low frequency resolution.  
Large window sizes give you good frequency resolution but bad time  
resolution. You can think of the original time-domain signals on the o- 
scope as shrinking the time window to be infestimally small, and  
having no frequency resolution. You can think of the Fourier transform  
as stretching the window to encompass the whole signal, and you have  
no time resolution.

When the students use a small time window, they see a single line at  
the average of two frequencies that blinks in and out at the beat  
rate. When they use a large time window, they don't see blinking -  
they see two solid lines, each at the actual frequencies.

When you're tuning your guitar, if the frequencies are close, you  
perceive the AM beats. As you tune them further apart, eventually you  
perceive the two tones.

I've probably just confused matters more. Anyway, that's my shot at  
another explanation. :)

- Aaron