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Question
Hey! I've been reading some of your answers and they seemed very clear so I wanted to ask if you could help me with this Waves question. Although I'm familiar with the concepts involved I'm lost as to how to apply them.

Two loudspeakers separated by 3.0 meters emit out-of-phase sound waves. Both speakers are playing a
686 Hz tone. If you are standing 4.0 meters directly in front of one of the loudspeakers. Do you hear
maximum sound intensity, minimum sound intensity, or something in between? Justify.

Answer
Hello,

If you use 343 m/s as the speed of sound, the formula lambda = v/f yields a wavelength of 0.5 m. The 2 speakers and where I'm standing make a 3-4-5 triangle. So I am standing 8 wavelengths from one speaker and 10 wavelengths from the other. If the speakers were in phase, the waves would reinforce each other and I would hear maximum sound intensity.

Since the speakers are out-of-phase, the skew, or phase angle, between the sound at my ears from the 2 speakers is the amount of phase angle between the drive to the 2 speakers. What I hear would not be maximum. The intensity would be minimum if the phase angle is 180 degrees but any other phase angle would yield something less than maximum -- in other words, something in between.

I hope this helps,
Steve

Physics

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Steve Johnson

Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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