Two speakers are separated by 3.0 meters and Joe stands 4.0 meters away in front
ID: 1506510 • Letter: T
Question
Two speakers are separated by 3.0 meters and Joe stands 4.0 meters away in front of one of the speakers as shown. The 2 speakers play a tone of 510 Hz in phase with each other.
a) Does Joe hear a louder or quieter sound than he would from only one speaker?
b) Now the frequency of the speakers is changed to 340 Hz, which leads to constructive interference where Joe stands. If he walks directly toward the nearer speaker, how far will he go before the sound is quietest?
c) If he continues toward the speaker, will there be another spot where the sound is maximum? Explain why or why not. (Hint: you should be able to answer this even if you can't do the calculation in part (b)).
Please explain these questions as thoroughly as possible, I am trying to grasp this question. Thank you so much!
2. Two speake rs are separated by 3.0 meters and Joe stands 4.0 meters away in front of one of the speakers as shown. The 2 speakers play a tone of 510 Hz in phase with each other. Does Joe hear a louder or quieter sound than he would from only 1 speaker? (b) Now the frequency of the speakers is changed to 340 Hz, which leads to constructive interference where Joe stands. If he walks directly toward the nearer speaker, how far will he go before the sound is quietest? (c) If he continues toward the speaker, will there be another spot where the sound is maximum? Explain why or why not. (Hint: you should be able to answer this even if you can't do the calculation in part (b)).Explanation / Answer
a) Distance from speaker 1 to joe = 4m
Distance from speaker 2 to joe = 5 m
Path difference = 1m
f = 510 Hz
lambda = 343/510 = 0.672549 m
path diff = 1.48688*lambda
so its is about 1.5 lambda (which is condition for detructive interefernce). so joe hears quiet sound
b) f = 340
d = 1 m
lambda = 343/340 = 1.0088 m
path diff = 0.99125 lambda = 1 lambda ( constructive intereference)
Distance moved towards nearer speaker = x
path diff = sqroot[(4 - x)^2 + 3^2] - (4 - x) = 1.5 lambda
16 + x^2 - 8x + 9 = [1.5*1.0088 + 4 - x]^2 = [5.5132 - x]^2 = x^2 + 30.39537 - 11.0264x
x = 1.7827 m
c) for next minima
path diff = sqroot[(4 - x)^2 + 3^2] - (4 - x) = 2.5 lambda
16 + x^2 - 8x + 9 = [2.5*1.0088 + 4 - x]^2 = [6.522- x]^2 = x^2 + 342.5364 - 13.044x
x = 62.95 m [ not posible]
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