Two waves are described by: y1 = 6 cos 180t and y2 = 6 cos 186t, (both in metres).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

Quizplus · Accepted Answer

The equation for the resultant wave is given by y = y1 + y2 = 6(cos 180t + cos 186t). Using the identity cos(a) + cos(b) = 2cos((a+b)/2)cos((a-b)/2), we can rewrite the equation as y = 12(cos(183t)cos(3t)). The amplitude of the wave is 12|cos(183t)|, which varies with time. The angular frequency at which the amplitude of the wave varies with time is 183 rad/s - 3 rad/s = 180 rad/s. Therefore, the answer is C.

Two Waves Are Described By: Y1 = 6 Cos 180t