Two speakers are placed at either end of a room, both pointing toward the center of the room, and equidistant from it. The speakers emit sound waves at 266 Hz, in phase with each other. a) How far apart are the anti-nodes of the standing sound wave created by this scenario? If a person walks across the room, from one speaker to the other, at 1.35 m/s, how much time does it take for them to travel from one anti-node to the next? b) If a person walks across the room, from one speaker to the other, at 1.35 m/s, what frequency of sound will they hear coming from each of the speakers (the one they are walking towards, and the one they are walking away from?) When these frequencies overlap, what will the beat frequency be? How much time elapses between the “beats” heard by the person walking across the room? 1) Draw a pictorial representation(s) of the problem. (You could use one overall, or one for each part of this two part problem.) 2) List the variables given, variables needed, and any simplifying assumptions being made. 3) Write out the general equations you will use to solve the standing wave part of the problem. 4) Solve part-a algebraically. 5) Write out the general equations you will use to solve the doppler and beats part of the problem. 6) Solve part-b algebraically. 7) Comment briefly on whether your result is reasonably believable. If it is – what sort of result could be easily identified as not believable for this problem?
Two speakers are placed at either end of a room, both pointing toward the center of the room, and equidistant from it. The speakers emit sound waves at 266 Hz, in phase with each other.
a) How far apart are the anti-nodes of the standing sound wave created by this scenario? If a person walks across the room, from one speaker to the other, at 1.35 m/s, how much time does it take for them to travel from one anti-node to the next?
b) If a person walks across the room, from one speaker to the other, at 1.35 m/s, what frequency of sound will they hear coming from each of the speakers (the one they are walking towards, and the one they are walking away from?) When these frequencies overlap, what will the beat frequency be? How much time elapses between the “beats” heard by the person walking across the room?
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1) Draw a pictorial representation(s) of the problem. (You could use one overall, or one for each part of this two part problem.)
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2) List the variables given, variables needed, and any simplifying assumptions being made.
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3) Write out the general equations you will use to solve the standing wave part of the problem.
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4) Solve part-a algebraically.
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5) Write out the general equations you will use to solve the doppler and beats part of the problem.
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6) Solve part-b algebraically.
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7) Comment briefly on whether your result is reasonably believable. If it is – what sort of result
could be easily identified as not believable for this problem?
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