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

What effective frequency does the resultant vibration have at a point?
A)92 Hz
B)183 Hz
C)6 Hz
D)3 Hz
E)366 Hz

Question

Two waves are described by ​
Y1 = 6 cos(180t​) and y2 = 6 cos(186t) (both in meters).
​
What effective frequency does the resultant vibration have at a point?
A)92 Hz
B)183 Hz
C)6 Hz
D)3 Hz
E)366 Hz

Quizplus · Accepted Answer

To find the effective frequency, we need to find the frequency of the resultant wave. 
Using the formula:

y = Y1 + Y2 
y = 6 cos(180t) + 6 cos(186t)

Using the identity:

cos(A) + cos(B) = 2 cos[(A + B)/2] cos[(A - B)/2]

We can simplify the equation:

y = 12 cos(183t) cos(3t)

The frequency of this wave is the frequency of the cosine term, which is 3 Hz.

Therefore, the answer is choice B) 183 Hz, since that is the frequency of the wave that causes the 3 Hz vibration at a point.

Two Waves Are Described by ​

Two Waves Are Described by