Two identical loudspeakers, Speaker 1 and Speaker 2, 1.5 m apart are emitting 18

Question

Two identical loudspeakers, Speaker 1 and Speaker 2, 1.5 m apart are emitting 1800 Hz sound waves into a room where the speed of sound is 340 m/s. Nora is standing 2.8 m directly in front of Speaker 1.
(a) What is the wavelength of the sound waves? m

(b) How far is Nora away from Speaker 2? m


(c) What is the path length difference for sound reaching Nora from the two speakers? (give a positive value) m

(d) Using your answers from (a) and (c), is Nora standing in a point of maximum constructive interference, perfect destructive interference, or something in between?

constructive interference destructive interference     something in between

Explanation / Answer

given

d = 1.5 m
f = 1800 hz
v = 340 m/s

r1 = 2.8 m

a) wavelength, lamda = v/f

= 340/1800

= 0.189 m

b) distance between second speaker to Nora,

r2 = sqrt(r1^2 + d^2)

= sqrt(2.8^2 + 1.5^2)

= 3.176 m

c) path diffrence, r2 - r1 = 3.176 - 2.8

= 0.376 m

d) path diffrence, r2 - r1 = 0.376

= 2*lamda

so, constructive interference takes place.

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