Two sound waves of the same frequency and amplitude are broadcast from speakers at opposite ends of a theater. In the middle of the theater, you hear a sound 6 dB louder than that from either speaker. Which of the following is true?

Question

anonymous · Answer

The two waves are 45° out of phase in the middle of the theater.

        The two waves are 90° out of phase in the middle of the theater.

        The two waves are 180° out of phase in the middle of the theater.

        The two waves are in phase in the middle of the theater.

radar · Answer

I would say the last choice is the better one.  They would be in phase assuming the two waves depart the speaker at the same phase.  Just because they are the same frequency does not insure they are the same phase.

anonymous · Answer

wouldn't they be 180 out of phase because they are at opposite ends?

radar · Answer

If they were 180 degrees out of phase, how would that result in an increase of 6 dB when they combine?

radar · Answer

keep in mind the distance from the sources to middle of the theater would be equal.  Any resulting phase change as a result of the time to arrive at the middle, would be the same for each.....wouldn't it?