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Solved: Beats and Standing Waves In 63, suppose the
Chapter 14, Problem 116GP(choose chapter or problem)
Problem 116GP
Beats and Standing Waves In Problem 63, suppose the observer walks toward one speaker with a speed of 1.35 m/s. (a) What frequency does the observer hear from each speaker? (b) What beat frequency does the observer hear? (c) How far must the observer walk to go from one point of constructive interference to the next? (d) How many times per second does the observer hear maximum loudness from the speakers? Compare your result with the beat frequency from part (b).
Reference Problem:
Two loudspeakers are placed at either end of a gymnasium, both pointing toward the center of the gym and equidistant from it. The speakers emit 266-Hz sound that is in phase. An observer at the center of the gym experiences constructive interference. How far toward cither speaker must the observer walk to first experience destructive interference?
Questions & Answers
QUESTION:
Problem 116GP
Beats and Standing Waves In Problem 63, suppose the observer walks toward one speaker with a speed of 1.35 m/s. (a) What frequency does the observer hear from each speaker? (b) What beat frequency does the observer hear? (c) How far must the observer walk to go from one point of constructive interference to the next? (d) How many times per second does the observer hear maximum loudness from the speakers? Compare your result with the beat frequency from part (b).
Reference Problem:
Two loudspeakers are placed at either end of a gymnasium, both pointing toward the center of the gym and equidistant from it. The speakers emit 266-Hz sound that is in phase. An observer at the center of the gym experiences constructive interference. How far toward cither speaker must the observer walk to first experience destructive interference?
ANSWER:
Step 1 of 4
(a)
Here we need to calculate the observed frequency from the speaker if the observer approaches one speaker with a speed . Let the speed of sound be
and the frequency of the speaker is
.
The heared frequency by the observer from the speaker when he approaches it,
It is given by,
Substituting ,
and
The heared frequency by the observer from the speaker when he moves away from it,
It is given by,
Substituting ,
and
Therefore, the observer hears a sound from the approaching speaker with frequency 267 Hz and a frequency of 265 Hz from the speaker from which he is moving away.