Your roommate has two loud speakers on either end of your 5 meter long dorm room

Question

Your roommate has two loud speakers on either end of your 5 meter long dorm room blaring mind-numbing bass tune at a constant 50 Hz. The desk where you study is at a point of constructiveinterference somewhere along the line joining the two speakers. How far do you need to move yourdesk to be located at a point of destructive interference? (Note: to help visualize the effect of havingspeakers at opposite ends of the room with waves traveling opposite directions, check out thisanimation: http://physics.uwyo.edu/~chip/Classes/PHYS1210/Slides/Day42/super3.gifâ€

Suppose now your room is located at the south pole on a cold day when the temperature is -100 C. Do you need to move your desk farther, or less far:? and by how much? Show a computation to back up your answer.

Explanation / Answer

LAMBDA = V / f = 343 / 50 = 6.86 m

for constructive = path diff = n *lambda for n= 0 pd = 0 he is at mid way i.e 2.5 m

for destructive = pd = (n+0.5) lambda n=0 he is at 3.43

distance to be moved = 3.43 - 2.5 = 0.93 m

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