What Distance from Speaker A Will a Microphone Detect Minimum Sound Intensity?

[patrickmoloney]

Homework Statement

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 )

Homework Equations

c=fλ,

The Attempt at a Solution

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

 

[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?

 

[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

 

[haruspex]

Distance is sqrt(1.96)+x².

That's not what you meant to write, I hope.

How do I calculate the wavelength at each point.

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.

lambda=c/f = 330/ 450 = 0.7333 which is all I know. I also know that destructive interference occurs at lamda/2

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?