Two sound sources and minimum sound points

[jmm5872]

Two sound sources 4 m apart have the same frequency of 880 Hz. The sources emit energy in the form of spherical waves. An observer initially hears a minimum sound, since the sound sources are out of phase, at a distance of 15 m along the perpendicular bisectorof the line joining the two sources. What distance x must the observer move along a line parallel to the line joining the two sources before hearing another sound of minimum intensity? THe speed of sound is 336 m/s.


I'm not even sure where to start for this problem. Do I need to find the equations for both the sound waves and find where they interfere deconstructively?

I would really appreciate any hints to get me started.

 

[jbsteele]

The answer to this question can be found by using the principle of superposition. Superposition states that the total effect of two or more waves at any point in space is the sum of their individual effects. In this case, the total sound intensity at any given point is the sum of the intensities of the two sources. To solve this problem, we need to find the distance between the observer and each sound source, and then calculate the phase difference between them. The phase difference is related to the distance between the observer and the two sources. If the phase difference is equal to an integer multiple of 2π, the two sources will be in phase and the observer will hear the maximum sound intensity. On the other hand, if the phase difference is equal to an odd multiple of π, the two sources will be out of phase and the observer will hear the minimum sound intensity. Now we can calculate the distance x that the observer must move along the line parallel to the line joining the two sources before hearing another sound of minimum intensity. This distance can be calculated as follows:x = (2πn + π)(v/f)where v is the speed of sound (336 m/s), f is the frequency of the sound (880 Hz), and n is any odd integer. Therefore, if n = 1, x = (2π + π)(336/880) = 0.75 m. If n = 3, x = (6π + π)(336/880) = 2.25 m. And so on.