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Constructive and destructive interefernec and a pair of speakers 
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#1
Mar308, 10:30 AM

P: 1,031

1. The problem statement, all variables and given/known data
Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q What is the lowest frequency for which constructive interference occurs at point ? What is the lowest frequency for which destructive interference occurs at point ? 2. Relevant equations not sure 3. The attempt at a solution I know that constructive occurs when waves are in phase, destructive when 180 degrees/pi radians out of phase Any ideas would be most appreciated Thanks, TFM 


#2
Mar308, 04:31 PM

P: 456

If speaker_a produces a signal sin(2*pi*f * t), what will be the signal at a point a distance d_a from a? This is just the same signal delayed by the time to get to the
distance d_a This will still be a sine wave so the signal looks like sin(2*pi*f*t  .........) speaker_b produces the same signal, so the same applies at a distance b_d from b. The total signal is just the signal from both speakers added. d_a and d_b are given in the problem 


#3
Mar408, 05:40 AM

P: 1,031

I am not sure what you mean by signal?
TFM 


#4
Mar508, 01:37 PM

P: 1,031

Constructive and destructive interefernec and a pair of speakers
Constructive Interference occurs at [tex] n\lambda [/tex]
Destructive Interference occurs at [tex] \frac{n}{2 \lambda}[/tex] Using the basic wave equation, speed = wavelength * frequency, they can be rearranged for frequency: Constructive Interference occurs at [tex] n(\frac{344}{f}) [/tex] Destructive Interference occurs at [tex] n(\frac{344}{2f}) [/tex] but I am unsure how I should proceed from now? (I hope this is relevant) Any help would be much appreciated, TFM 


#5
Mar508, 04:00 PM

P: 1,031

Looked in my book, fpuind the right equation:
constructive: [tex] f_n = \frac{nv}{d} [/tex] destructive: [tex] f_n = \frac{nv}{2d} [/tex] where d is the path difference. TFM 


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