Two loudspeakers are placed 4.5 m apart. They produce the same sounds, in step,

Question

Two loudspeakers are placed 4.5 m apart. They produce the same sounds, in step, at a frequency of 829 hz. Constructive interference is observed a point P, which is located 5.3 m from one loudspeaker and a distance x from the other. What is a possible value of x? Assume the speed of sound is 340 m/s. A) 6.8 m B) 6.77 m C) 6.53 m D) 6.6 m E) 6.88 m
Two loudspeakers are placed 4.5 m apart. They produce the same sounds, in step, at a frequency of 829 hz. Constructive interference is observed a point P, which is located 5.3 m from one loudspeaker and a distance x from the other. What is a possible value of x? Assume the speed of sound is 340 m/s. A) 6.8 m B) 6.77 m C) 6.53 m D) 6.6 m E) 6.88 m
A) 6.8 m B) 6.77 m C) 6.53 m D) 6.6 m E) 6.88 m

Explanation / Answer

wavelength of the sound wave lambda = v/f

v = speed of the sound wave

f = frequency emitted

for constructive interference path difference r2 - r1 = m*lambda

r2 - r1 = m*v/f

x - 5.3 = m*340/829

for m = 1

x - 5.3 = 1*340/829

x = 5.71 m

for m = 2

x - 5.3 = 2*340/829

x = 6.12 m

for m = 3

x - 5.3 = 3*340/829

x = 6.53 m

for m = 4

x - 5.3 = 4*340/829

x = 6.94 m

OPTION (C) <<<<-------answer

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