What is the effect of combining two sinusoidals with different frequencies?

[Physics2013]

Homework Statement

Find the frequency of the combined motion of sin(3t) - cos(Pi t)

Homework Equations

Cos(A) - Cos(B) = -2sin([A+B]/2)sin([A-B]/2)
f=1/T
Omega=2Pi/T

The Attempt at a Solution

sin(3t) - cos(Pi t) =
cos(3t - (Pi/2)) - cos(Pi t) =
-2sin({t[3 + pi]/2} - (pi/4))sin({t[3 - pi]/2} - (pi/4))

Now, I tried taking the average of omega(1) and omega(2), but this is not correct.
I am confused on what the next step is.

 

[gabbagabbahey]

Homework Statement

Find the frequency of the combined motion of sin(3t) - cos(Pi t)

Homework Equations

Cos(A) - Cos(B) = -2sin([A+B]/2)sin([A-B]/2)
f=1/T
Omega=2Pi/T

The Attempt at a Solution

sin(3t) - cos(Pi t) =
cos(3t - (Pi/2)) - cos(Pi t) =
-2sin({t[3 + pi]/2} - (pi/4))sin({t[3 - pi]/2} - (pi/4))

Now, I tried taking the average of omega(1) and omega(2), but this is not correct.
I am confused on what the next step is.

When you have two sinusoidals multipled together, and the frequency of one is much larger/faster than the frequency of the other, the overall signal appears to oscillate at the smaller/slower frequency, and is modulated by the much faster sinusoid (you end up with a "bumpy" sinusoid where the bumps have a very fast frequency, but their amplitude is much smaller and they are often almost unnoticable). Try graphing your signal over a very short (much less than the period of the slower sinusoid) and a longer (at least ione full period of the slower sinusoid) time interval to better visualize what's going on.