- #1

hidemi

- 208

- 36

- Homework Statement
- Two waves are described by y1 = 6 cos 180 t and y2 = 6 cos 186 t (both in meters). What effective frequency does the resultant vibration have at a point?

92 Hz B)183 Hz. C)6 Hz. D)3 Hz. E)366 Hz

The correct answer is B

- Relevant Equations
- Y=−2Acos(At)cos(2πft)

Explanation:

y1=6cos(180t)

y1+y2 =6cos(180t)+6cos(186t)y

=6(cos(180t)+cos(186t))

cos(A)+cos(B)=−2cos((A+B)/2)cos((A−B)/2)

y=6(−2cos((180+186)t/2)cos((180−186)t/2))

y=−12cos(183t)cos(3t)

y=(−12cos(3t))cos(183t)

Comparing with the standard equation,

Y=−2Acos(At)cos(2πft)

Therefore we have by comparison that,

2πf=183f=1832π

∴f=29.1Hz. This is my answer. I could not find a matching answer. Where am I doing wrong?

y1=6cos(180t)

__＋） y2=6cos(186t)__y1+y2 =6cos(180t)+6cos(186t)y

=6(cos(180t)+cos(186t))

cos(A)+cos(B)=−2cos((A+B)/2)cos((A−B)/2)

y=6(−2cos((180+186)t/2)cos((180−186)t/2))

y=−12cos(183t)cos(3t)

y=(−12cos(3t))cos(183t)

Comparing with the standard equation,

Y=−2Acos(At)cos(2πft)

Therefore we have by comparison that,

2πf=183f=1832π

∴f=29.1Hz. This is my answer. I could not find a matching answer. Where am I doing wrong?