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Question

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To practice Problem-Solving Strategy 21.1 for wave interference problems.

Two loudspeakers are placed side by side a distance d= 4.00m apart. A listener observes maximum

A)

The picture to the left shows the situation described in this problem. The upper speaker is initially at the same distance from the listener as the other speaker. Then, it is moved upward a distance r = 60.0cm . The dashed outline represents its new position. Note that r1 is the distance between the listener and the speaker that has not been moved, whereas r2 is the distance between the listener and the speaker that has been moved. Calculate r1 and r2.(Figure 1)

B)

What is the phase difference ??0 between the sound waves reaching the listener's ear initially, before the upper speaker is moved?

Express your answer numerically, in terms of ? if necessary.

Explanation / Answer

r1= ?(2^2+5^2)= 5.385m
r2= ?(2.6^2+5^2)= 5.635m
L= r2-r1 = 0.25m
?=2L = 2*0.25= 0.5m
v= f? = 700*0.5= 350m/s
t= (350-331.3)/0.606= 30.85= 31[?]

constructive interference r2-r1= ?= 0.5m
r2= r1+0.5= 5.385+0.5= 5.885m
5.885^2=5^2+x^2
x=?(34.63-25)= 3.103m
r= 3.10-2= 1.1[m] (new r)

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