Two small loudspeakers that are 5.50 apart are emitting sound in phase. From bot

Question

Two small loudspeakers that are 5.50 apart are emitting sound in phase. From both of them, you hear a singer singing C# (frequency 277 ), while the speed of sound in the room is 340 . Assuming that you are rather far from these speakers, if you start out at point equidistant from both of them and walk around the room in front of them, at what angles (measured relative to the line from to the midpoint between the speakers) will you hear the sound: cancelled? Neglect any reflections from the walls.

Explanation / Answer

= c/f = 340/277 = 1.227 m

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destructive interference:

d sin = (m + 1/2)

>>>>> = arcsin{(m + 1/2)*(/d)}

for m = 0 >>>> = arcsin{(1/2)*(1.227/5.5)} = 6.40 degrees

for m = 1 >>>> = arcsin{(3/2)*(1.227/5.5)} = 19.55 degrees

for m = 2 >>>> = arcsin{(5/2)*(1.227/5.5)} = 33.90 degrees

for m = 3 >>>> = arcsin{(7/2)*(1.227/5.5)} = 51.34 degrees

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