# Intensity of Sound Waves

1. Nov 21, 2013

### patrickmoloney

1. The problem statement, all variables and given/known data

Two loudspeakers A and B of equal power are separated by a distance of 1.4 m. Both the speakers emit sound waves in phase and of frequency 450 Hz. If a microphone were to be moved from A in a direction perpendicular to AB, at what distances from A will it detect a minimum of sound intensity? ( Take the velocity of sound in air to be 330 m/s )

2. Relevant equations

c=fλ,

3. The attempt at a solution

I have no idea where to even start. I tried using Pythagoras' theorem and could go no further.

2. Nov 21, 2013

### haruspex

Pythagoras' theorem is certainly relevant.
At a point distance x from A along that line, how far is it from B?
How many wavelengths is it from each? What will the phase difference be at that point?

3. Nov 21, 2013

### patrickmoloney

Distance is sqrt(1.96)+x². How do I calculate the wavelength at each point. lambda=c/f = 330/ 450 = 0.7333 which is all I know. I also know that destructive interference occurs at lamda/2

4. Nov 21, 2013

### haruspex

That's not what you meant to write, I hope.
I did not suggest calculating a wavelength at each point. There is only one wavelength, which you have calculated. I said to calculate the number of wavelengths represented by each of the two distances. But the alternative below may be simpler.
For sources in phase, same frequency, completely destructive interference occurs when the difference in the path lengths is lambda/2. What, as a function of x, is the difference in the path lengths? How many wavelengths is that?