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Homework Help: Sum of two cosine functions with angular frequences

  1. Mar 10, 2010 #1

    bon

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    1. The problem statement, all variables and given/known data

    ok so im given that I(t) = A cos (w1 t)cos(w2 t)

    where w2<<w1

    then im asked to express I as the sum of two cosine functions with angular frequences P and Q which I have:

    I = A/2 (cosPt + cosQt) where P = w1+w2 and Q=w1-w2

    Im then asked to evaluate the bandwith in terms of w1 and w2

    Is this just |P-Q| in which case it would be 2w2? im confused :S thanks

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 10, 2010 #2
    Re: bandwith

    Yes, it is confusing. Because Bandwidth=|P-Q| is wrong! Without additional qualification it gives you two mutually inconsistant answers.

    Let's pick two frequencies. w1=10 and w2=100.

    Q = w1-w2 = -90, and we have a negative frequency.
    P = 110, and the bandwidth would be 110 - -90 = 200.

    Swap roles.

    w1=100
    w2=10

    Now Q = 90 and P = 110.

    The bandwith according to |P-Q| = 20.

    How would you express your solution to ensure that Q and P are both positive valued?
     
    Last edited: Mar 10, 2010
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