Answer
a. 0.562 m.
b. 0 m.
Work Step by Step
a. Let the 2 speakers be separated by a distance L.
Because the 2 speakers emit sounds that are 180 degrees out of phase, if a person stands directly in front of a speaker, there will be constructive interference if the distance L to the other speaker is half a wavelength,three half wavelengths, five half wavelengths, etc.
We seek the minimum distance L.
$$L=\frac{\lambda}{2}=\frac{v}{2f}=\frac{343m/s}{2(305Hz)}=0.562m$$
If the distance L were to slowly increase, the location of constructive interference moves away from the speaker, toward the other speaker.
b. The sounds are 180 degrees out of phase. If a point is the same distance from both speakers, the waves arriving there will exhibit completely destructive interference. The minimum separation between the speakers is L = 0 meters.
