Calculating Bandwidth of AM Signal with Dual Cosine Modulation

[Shackman]

Homework Statement

What is the bandwidth of an AM signal if the modulating signal is
x(t)=cos(2pi70t)+cos(2pi90t) and the carrier frequency is 10kHz?

Homework Equations

The Attempt at a Solution

The carrier frequency is irrelevant because it just means the signal's spectrum is concentrated around it, it has no bearing on bandwidth. I know that bandwidth of an AM signal is two times the baseband bandwidth. However, I am not sure what that would be here because you are summing cosines with different frequencies. If only one cosine was present, the bandwidth would be two times its frequency, but as there are two I don't know what to do. My guess is that the smaller frequency (larger period) prevails as it would dominate the higher frequency component.

 

[xcvxcvvc]

there are many ways to define "bandwidth." If it means the highest frequency minus the lowest frequency (that is nonnegative), a cosine alone would have 0 bandwidth. Also, two sinusoids would have a bandwidth equal to the frequency of the faster sinusoid minus the frequency of the slower sinusoid.

90 - 70 = 20