Two waves are described by
Y₁ = 6 cos 180t and y₂ = 6 cos 186t, (both in meters) .
With what angular frequency does the maximum amplitude of the resultant wave vary with time?

Question

Quizplus · Accepted Answer

The resultant wave can be found as follows:
yS1U1B0 = yS1U1B11S1U1B0 + yS1U1B12S1U1B0
yS1U1B0 = 6 cos 180t + 6 cos 186t
Using the trigonometric identity, cos(A+B) = cosA cosB - sinA sinB, we can rewrite yS1U1B0 as:
yS1U1B0 = 12 cos(3t) sin(3t + θ)
where θ is some constant phase angle.
The amplitude of this wave is given by 12 cos(θ), and it varies with time due to the presence of the sin(3t + θ) term. This term has an angular frequency of 3 radians per second, which means that the maximum amplitude of the resultant wave varies with time at this frequency. Therefore, the answer is (C) 3 rad/s.

Two Waves Are Described by