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Old Oct 14th 2017, 05:50 AM   #1
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Beating problem

I am trying to understand beating of two sinusoidal waves and have a fundamental problem with spotting on simulations the combined frequency of two waves that is supposed to be the average of the two interfering. Below is attached a Matlab screenshot where from the top there is x1, x2, x1+x2 defined as:
t=1:0.1:6;
x1=sin(2*pi*t);
x2=sin(3*pi*t);
I can easily see the differential beating envelope but no clue how the average combined frequencey is reflected on the graph e,g, when I count the zero crossings I rather get the higher of the two component frequencies,
Regards, Pawel
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Beating problem-beating_2_3pi.png  
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Old Oct 14th 2017, 10:11 AM   #2
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$T = \dfrac{2\pi}{\omega} \implies f = \dfrac{\omega}{2\pi}$


$T_{x_1} = 1 \implies f_{x_1} = 1$

$T_{x_2} = \dfrac{2}{3} \implies f_{x_2} = \dfrac{3}{2}$

$f_b = |f_{x_2}-f_{x_1}| = \dfrac{1}{2} \iff T_b = 2$

attached graph shows two periods of $x_1+x_2$ ...
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Beating problem-sinusoid_sum.jpg  
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Old Oct 14th 2017, 11:43 AM   #3
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Originally Posted by skeeter View Post
$T = \dfrac{2\pi}{\omega} \implies f = \dfrac{\omega}{2\pi}$


$T_{x_1} = 1 \implies f_{x_1} = 1$

$T_{x_2} = \dfrac{2}{3} \implies f_{x_2} = \dfrac{3}{2}$

$f_b = |f_{x_2}-f_{x_1}| = \dfrac{1}{2} \iff T_b = 2$

attached graph shows two periods of $x_1+x_2$ ...
Yes, the graph shows the addition but does the post is aimed to explain how to visually spot/identify the averaging of two sinusoidal frequencies when combined ?
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Old Oct 14th 2017, 12:30 PM   #4
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The graph shows the period of the combined sinusoids, from which the frequency can be determined.
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Old Oct 15th 2017, 12:01 AM   #5
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Originally Posted by skeeter View Post
The graph shows the period of the combined sinusoids, from which the frequency can be determined.
As per on the definitions:
This resulting particle motion is the product of two travelling waves. One part is a sine wave which oscillates with the average frequency fa = (f1 + f2). This is the frequency which is perceived by a listener. The other part is a cosine wave which oscillates with the difference frequency fd = (f1 - f2). This term controls the amplitude "envelope" of the wave and causes the perception of "beats". The beat frequency is actually twice the difference frequency, fbeat = (f1 - f2)."

The frequecny that you showed as far as I can tell corresponds to the difference frequency fd but I cannot find any trace of the average frequency fa
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