Two speakers, emitting identical sound waves of wavelength 1.4 m in phase with e

Question

Two speakers, emitting identical sound waves of wavelength 1.4 m in phase with each other, and an observer are located as shown in the figure below. (Let x = 8.0 m, and y= 10.0 m.)

(a) At the observer's location, what is the path difference for waves from the two speakers?
m

(b) Will the sound waves interfere constructively or destructively at the observer's location?

constructivedestructive     

(c) Suppose the observer now increases her distance from the speakers to 45.4 m, staying directly in front of the same speaker as initially. What is the path difference for waves from the two speakers?
m

Will the sound waves interfere constructively or destructively at the observer's location?

constructivedestructive

Explanation / Answer

a)

here

path length difference = sqrt( 10^2 + 8^2) - 10 = 2.8 m

b)

at the observer's location sound wave interfere constructive

c)

sqrt(45.4^2 + 8^2) = 46

then

46 - 45.4 = 0.6 m

which is approx half the wavelength

the sound waves interfere destructively at the observer's location

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