5. Two stationary speakers are separated a distance of d = 2 m. Both speakers produce spherical sound waves with a frequency of 550 Hz and both speakers supply the same average power of 400 W. The air temperature is 20°C. d >) (8)) X OK Alice stands equidistance from both speakers a distance x = 20 m to the right. a) What sound level will Alice hear if the waves constructively interfere at her location? If Bob is directly to the right of Alice and hears a sound level of 10 dB, how far apart are Bob and Alice? b) Suppose the speakers have the same initial phase, but the top speaker is turned on 2.001 s before the bottom speaker. What type of interference will Alice observe? Constructive, destructive, or something in-between? c) Suppose the top speaker is again turned on 18.191 s before the bottom speaker, but now the bottom speaker begins with a different initial phase. If Alice observes constructive interference at her location, what is the difference between the initial phases of the speakers? d) Now suppose both speakers are turned on at the same time and with the same initial phase. Alice walks directly towards the top of the page. How far must Alice walk until she observes destructive interference for the second time? How far must she walk to observe constructive interference for the second time (excluding her initial location)? e) For this part, Alice again starts equidistant from the speakers a distance to the right and walks directly towards the top of the page. However, someone changed the settings on the speakers. Now, the bottom begins a quarter cycle ahead of the top speaker, and the frequency of the sound is unknown. Alice hears destructive interference for the first time after walking 5 m. What is the frequency of the sound?
5. Two stationary speakers are separated a distance of d = 2 m. Both speakers produce spherical sound waves with a frequency of 550 Hz and both speakers supply the same average power of 400 W. The air temperature is 20°C. d >) (8)) X OK Alice stands equidistance from both speakers a distance x = 20 m to the right. a) What sound level will Alice hear if the waves constructively interfere at her location? If Bob is directly to the right of Alice and hears a sound level of 10 dB, how far apart are Bob and Alice? b) Suppose the speakers have the same initial phase, but the top speaker is turned on 2.001 s before the bottom speaker. What type of interference will Alice observe? Constructive, destructive, or something in-between? c) Suppose the top speaker is again turned on 18.191 s before the bottom speaker, but now the bottom speaker begins with a different initial phase. If Alice observes constructive interference at her location, what is the difference between the initial phases of the speakers? d) Now suppose both speakers are turned on at the same time and with the same initial phase. Alice walks directly towards the top of the page. How far must Alice walk until she observes destructive interference for the second time? How far must she walk to observe constructive interference for the second time (excluding her initial location)? e) For this part, Alice again starts equidistant from the speakers a distance to the right and walks directly towards the top of the page. However, someone changed the settings on the speakers. Now, the bottom begins a quarter cycle ahead of the top speaker, and the frequency of the sound is unknown. Alice hears destructive interference for the first time after walking 5 m. What is the frequency of the sound?
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Transcribed Image Text:5. Two stationary speakers are separated a distance of d = 2 m. Both speakers produce spherical sound waves with a
frequency of 550 Hz and both speakers supply the same average power of 400 W. The air temperature is 20˚C.
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X
옷
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Alice stands equidistance from both speakers a distance x = 20 m to the right.
a) What sound level will Alice hear if the waves constructively interfere at her location? If Bob is directly to the right of
Alice and hears a sound level of 10 dB, how far apart are Bob and Alice?
b) Suppose the speakers have the same initial phase, but the top speaker is turned on 2.001 s before the bottom speaker.
What type of interference will Alice observe? Constructive, destructive, or something in-between?
c) Suppose the top speaker is again turned on 18.191 s before the bottom speaker, but now the bottom speaker begins
with a different initial phase. If Alice observes constructive interference at her location, what is the difference between
the initial phases of the speakers?
d) Now suppose both speakers are turned on at the same time and with the same initial phase. Alice walks directly
towards the top of the page. How far must Alice walk until she observes destructive interference for the second time?
How far must she walk to observe constructive interference for the second time (excluding her initial location)?
e) For this part, Alice again starts equidistant from the speakers a distance x to the right and walks directly towards the
top of the page. However, someone changed the settings on the speakers. Now, the bottom begins a quarter cycle ahead
of the top speaker, and the frequency of the sound is unknown. Alice hears destructive interference for the first time after
walking 5 m. What is the frequency of the sound?
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