Two identical loudspeakers 2.0 m apart are emitting 1800 Hzsound waves into a ro

Question

Two identical loudspeakers 2.0 m apart are emitting 1800 Hzsound waves into a room where the speed of sound is 340 m/s. Is thepoint 4.0 m directly in front of one of the speakers, perpendicularto the plane of the speakers, a point of maximum constructiveinterference, perfect destructive interference or something inbetween? Can someone please help me with this problem? Thanks inadvance will rate!!! Two identical loudspeakers 2.0 m apart are emitting 1800 Hzsound waves into a room where the speed of sound is 340 m/s. Is thepoint 4.0 m directly in front of one of the speakers, perpendicularto the plane of the speakers, a point of maximum constructiveinterference, perfect destructive interference or something inbetween? Can someone please help me with this problem? Thanks inadvance will rate!!!

Explanation / Answer

First, you need to find delta r, the difference between the point directly in front of one of the speakers and the distance from that point to the other speaker. The speakers are in the straight line and the given 4.0 m. point is directly in front of the one of the speakers so all together two speakers and the point form a straight triangle. Find the hypotenuse: 2^2+4^2=Sqrt20=4.47 To find delta r =4.47-4=0.47 m We also need to find the wavelength lambda=V/f=340/1800=0.188 we know that if the interference is constructive delta r/lambda is going to be a whole number and if it is destructive it is going to be only a half 0.47/0.188=2.5 which is 2+0.5 we should treat is a half of the whole number therefore it is a perfect destructive intenference

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