# [SOLVED] Constructive and destructive interefernec and a pair of speakers

by TFM
Tags: constructive, destructive, interefernec, pair, solved, speakers
 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
 P: 457 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
 P: 1,031 I am not sure what you mean by signal? TFM
P: 1,031

## [SOLVED] Constructive and destructive interefernec and a pair of speakers

Constructive Interference occurs at $$n\lambda$$

Destructive Interference occurs at $$\frac{n}{2 \lambda}$$

Using the basic wave equation, speed = wavelength * frequency, they can be rearranged for frequency:

Constructive Interference occurs at $$n(\frac{344}{f})$$

Destructive Interference occurs at $$n(\frac{344}{2f})$$

but I am unsure how I should proceed from now?

(I hope this is relevant)

Any help would be much appreciated,

TFM
 P: 1,031 Looked in my book, fpuind the right equation: constructive: $$f_n = \frac{nv}{d}$$ destructive: $$f_n = \frac{nv}{2d}$$ where d is the path difference. TFM

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