Adventures in Parallel Dimension #1729 II

Celebrating the success of parallel dimension #1729's discovery of the Biggs Hoson, CALVIN National Laboratories received a large amount of money and decided to build a REALLY big recreational room with a home theater.

The main features are a huge \(w=100 \text{ m}\) wide TV, and a state of the art sound system driven in phase at \(1000\text{ W RMS}\) that emits from directly below either end of the TV at a wavelength of \(\lambda=1\text{ m}\). A \(d=1\text{ km}\) long couch is going to be placed parallel to the TV at a distance of \(l=10\text{ m}\) from the front end of both speakers.

The architects failed to consider that the material used will cause everything in the room to absorb all of the sound that hits it, so all that anyone will hear are the sound waves directed exactly towards them from the pair of speakers. The physicists there, having a good sense of humor, have decided to play a joke on Greg by assigning him a spot on the couch where he won't be able to hear anything being emitted from the speakers. How many possible spots on the couch are there to place Greg?

Details and Assumptions:

  • Assume that the speakers have range to reach every spot on the couch.
  • Greg is part of a previously failed cloning experiment, so now he's a point mass.
  • The speed of sound through air in parallel dimension #1729 is \(340.29 {\text{ m/s}}.\)
  • Image is not drawn to scale.

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