Two waves are described by
Y1 = 6cos(180t) and y2 = 6cos(186t) (both in meters).

With what angular frequency does the maximum amplitude of the resultant wave vary with time?
A)366 rad/s
B)6 rad/s
C)3 rad/s
D)92 rad/s
E)180 rad/s

Question

Two waves are described by ​
Y1 = 6cos(180t) and y2 = 6cos(186t) (both in meters).
​
With what angular frequency does the maximum amplitude of the resultant wave vary with time?
A)366 rad/s
B)6 rad/s
C)3 rad/s
D)92 rad/s
E)180 rad/s

Quizplus · Accepted Answer

The resultant wave is given by y= y1 + y2 = 6cos(180t) + 6cos(186t). Using the identity cos(A) + cos(B) = 2cos((A+B)/2)cos((A-B)/2), we can simplify this to y = 12cos(183t)cos(3t). The amplitude of this wave varies as 12cos(3t), so the angular frequency with which the maximum amplitude varies with time is 3 rad/s.

Two Waves Are Described by ​

Two Waves Are Described by