Moe, Larry, and Curly stand in a line with a spacing of d = 0.800 m . Larry is 3
ID: 1618879 • Letter: M
Question
Moe, Larry, and Curly stand in a line with a spacing of d = 0.800 m . Larry is 3.00 m in front of a pair of stereo speakers 0.800 m apart, as shown in the figure(Figure 1) . The speakers produce a single-frequency tone, vibrating in phase with each other.
Part A
What are the two lowest frequencies that allow Larry to hear a loud tone while Moe and Curly hear very little?
Express your answers using two significant figures separated by a comma.
Moe, Larry, and Curly stand in a line with a spacing of d = 0.800 m . Larry is 3.00 m in front of a pair of stereo speakers 0.800 m apart, as shown in the figure(Figure 1) . The speakers produce a single-frequency tone, vibrating in phase with each other.
Part A
What are the two lowest frequencies that allow Larry to hear a loud tone while Moe and Curly hear very little?
Express your answers using two significant figures separated by a comma.
f = kHz 0.800 m 3.00 m Curly Larry MoeExplanation / Answer
If Larry is standing in the middle then Moe and Curly are each standing 0.8 m away from him. You have to find the distance between each speaker and either Moe or Curly. Draw a line from each speaker to Moe and call them X1 and X2 (the distances will be the same for either Moe or Curly). To find X1 (from the closer speaker):
X1=sqrt(L^2+y^2)
y = 0.8 - 0.4= 0.4 m because Larry is standing in the middle of the 2 speakers you can find the vertical distance between Moe/Curly and the speakers
X1 = sqrt(32 + 0.42) = 3.02 m
X2 is from the speaker that's farther away:
X2=sqrt(L^2+z^2)
z=0.8 + 0.4= 1.2 m
X2 = sqrt(32 + 1.22) = 3.23 m
since Curly and Moe can't hear the sound, it's destructive interference and the difference in the path length will have to equal 1/2( ). If it were constructive the path distance would equal
X2 - X1 = 1/2( )
2(X2 - X1) =
= 2(3.23 - 3.02) = 0.422
velocity v = 343 m/s
frequency f = v / = 343 / 0.422 = 812.41 Hz = 0.812 kHz
1/2(lambda) is the first lowest frequency, the next is 3/2().
X2 - X1 = 3/2( )
= (2/3)*(3.23 - 3.02) = 0.14
frequency f = v/ = 343 / 0.14 = 2450 Hz = 2.45 kHz
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