In my textbook, when two waves of the form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] y_1 = A\cos \left( 2\pi f_1t \right)[/tex]

[tex] y_2 = A\cos \left( 2\pi f_2t \right)[/tex]

combine, the following trig identity is used:

[tex] \cos a + \cos b = 2\cos \left( \dfrac{a-b}{2} \right) \cos \left( \dfrac{a+b}{2} \right) [/tex]

which yields an expression for y:

[tex]y=\left[ 2A\cos 2\pi \left( \dfrac{f_1-f_2}{2} \right) t \right] \cos 2\pi \left( \dfrac{f_1+f_2}{2} \right) t [/tex]

and thus the Amplitude for the resultant wave is the expression in the square brackets. BUT...why can't the order be switched, yielding:

[tex]y=\left[ 2A\cos 2\pi \left( \dfrac{f_1+f_2}{2} \right) t \right] \cos 2\pi \left( \dfrac{f_1-f_2}{2} \right) t [/tex]

Which seems to be a different wave with a different amplitude... What's going on here? Why am I forced to use this expression for the amplitude rather than the other one?

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# Homework Help: Amplitude of Two Waves in Interference

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