Solution is provided in \"(Solution)\". Please show all work. Two identical spea

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Solution is provided in "(Solution)". Please show all work.

Two identical speakers are mounted on a wall and separated by 4.16 m. They emit sounds of same frequency of 229 Hz. Will a person A hear constructive or destructive interference? (use the condition for interference) (Constructive or loud sound, prove it) Will person B hear constructive or destructive interference? (use the condition for interference) (Constructive or loud sound, prove it) Two identical loudspeakers separated by distance demit 170 Hz sound waves along the x-axis. As you walk along the axis, away from both of the speakers, you don't hear anything even though both speakers are on. What are the three smallest possible values for d for this to be the case? Assume a sound speed of 340 m/s.(1m, 3m, 5m) Two source of sound having wavelengths 0.7 m and 0.88 m are sounded together. What beat frequency is heard? (100 Hz) Suppose I have two speakers, separated by 5.09 m, each emitting an 800 Hz sound, and I listen at a point 30.0 m away as shown (not to scale). Use v = 343 m/s. Assume that the speakers are in phase-that is they both emit a peak at the same time. What will I hear, constructive or destructive interference? (loud, why? Prove it) Now I move the bottom speaker vertically up. At what speaker separation will I hear the other type of interference from part (a)? (3.59 m) Suppose I double the frequency of the speakers, what will I hear for the two separations in a) and b) above? (loud for both (a) and (b) but prove it)

Explanation / Answer

1)
a) path difference of two waves at point A = 0

so, the person hears constructive ineterefeernce.

b)

v = 340 m/s
v = lamda*f

==>lamda = v/f = 340/229 = 1.5 m

r2 = sqrt(5^2+4.16^2) = 6.5 m

r1 = 5 m

r2 - r1 = 1.5 m

so, person b also hears constructive inerference.

2)
lamda = v/f = 340/170 = 2 m

for ditructive interference

so, d = (m + 1/2)lamda (m=0,1,2,3,4,5,..)

d = 1m,3m,5m,7m...

3)

f1 = v/lamda1 = 340/0.7 = 485.7

f2 = v/lamda2 = 340/0.88 = 386.4

fbeat = f1-f2 = 100 (approximately)

4)
lamda = v/f = 343/800 = 0.42875 m

a) r1 = 30 m

r2 = sqrt(5.09^2 + 30^2) = 30.42875

r2-r1 = 0.42875 m = lamda

so, you here constructive interference

b)

r2 = 30 m

r1 = sqrt(5.09^2 + 30^2) = 30.42875

r1-r2 = 0.42875 m = lamda

so, you here constructive interference

c) in both cases you here a loud sound.

proof.11:46 AM 11/26/2013

lamda = v/f = 343/1600 = 0.214375

a) r1 = 30 m

r2 = sqrt(5.09^2 + 30^2) = 30.42875

r2-r1 = 0.42875 m = 2*lamda

so, you here constructive interference

b)

r2 = 30 m

r1 = sqrt(5.09^2 + 30^2) = 30.42875

r1-r2 = 0.42875 m = 2*lamda

so, you here constructive interference

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