Sum of two cosine functions with angular frequences

[bon]

Homework Statement

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

where w2<<w1

then I am 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? I am confused :S thanks

Homework Equations

The Attempt at a Solution

 

[Phrak]

Homework Statement

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

where w2<<w1

then I am 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? I am confused :S thanks

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?