Analyze beats using complex exponentials

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The discussion focuses on evaluating the expression e^(iω1t) + e^(iω2t) using complex algebra. Participants emphasize that the sum of two frequencies creates beats, which can be represented as the real part of the complex exponentials. A user attempts to convert the expression into cosine and sine terms but is advised to express the answer in terms of p and q, where p = (ω1 + ω2)/2 and q = (ω1 - ω2)/2. The importance of using complex exponentials rather than relying solely on trigonometric identities is highlighted. The conversation encourages a deeper understanding of the relationship between frequency and waveforms in sound.
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Homework Statement



Please use the complex algebra to evaluate e^(iω1t)+e^(iω2t), w2 means omega 2?


Homework Equations


Ho do I do this problem


The Attempt at a Solution


I changed this into cos and sine terms.
 
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ωelcome to PF!

Hi Lizwi! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 


Thaks, They said: beats occur in sound when two sources emit frequencies that are almost the same. The perceived wave is the sum of the two waves, so that at your ear, the wave is the sum of the two cosines of w1t and w2t...( my w means omega ) use complex algebra two evaluate this. The sum is the real part of e^(w1t)+e^(w2t). notice the two identities w1= (w1+w2)/2 + (w1-w2)/2. Use the complex exponentials to drive the results; dont't just look up some trig identity.


What I did is , because they said the sum is the real part of e^(w1t)+e^(w2t) I wrote this in term of course and sine: (cosw1t + i sinw1t) + (cosw2t + i sinw2t)
(cosw1t + cosw2t) + i (sinw1t + sinw2t)
the real part is cosw1t + cosw2t
Im done!
 
(try using the X2 button just above the Reply box :wink:)
Lizwi said:
The sum is the real part of e^(w1t)+e^(w2t). notice the two identities w1= (w1+w2)/2 + (w1-w2)/2. Use the complex exponentials to drive the results; dont't just look up some trig identity.
…
Im done!

noooo, you're not! :redface:

read the hint …

they want you to write the answer in terms of p and q, where p = (w1+w2)/2 and q = (w1-w2)/2

try again :smile:​
 
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