# Constructive and destructive interefernec and a pair of speakers

1. Mar 3, 2008

### TFM

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

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. Mar 3, 2008

### kamerling

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. Mar 4, 2008

### TFM

I am not sure what you mean by signal?

TFM

4. Mar 5, 2008

### TFM

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

5. Mar 5, 2008

### TFM

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