needing help with this old physics problem

Question

Two sound waves W1 and W2 of the same wavelength interfere destructively at point P. The waves originate from two in phase speakers. W1 travels 36m and W2 travels 24m before reaching point P. Which of the following values could be the wave length of the sound waves?

6m

4m

24m

12m

Answer 1

Hi Ian C.,

Destructive interference means that one of the sound waves is exactly out-of-phase with the other. It's fairly easy to see that 24 m meets this criterion, since the difference in travel distance (12m) is exactly one half of that wavelength. Does this mean that you would detect NO sound for 24m waves? Not exactly, since the 24m-away speaker will be louder than the 36m-away speaker. Assuming 2D-propagation would put the weaker speaker at 4/9 the strength of the stronger one; if the speakers radiate to a 3D hemisphere, the weaker speaker is only 8/27 as strong as the stronger one. That would still be a noticable weakness in the frequency spectrum, but not a fatal one for listening to music, since music is usually: 1) stereo, 2) has harmonics to the notes, and 3) has acoustic changes due to the room shape and objects therein.

But, for a real treat, check out audio-over-microwave transmission. The audio wave is used to modulate a water-vapor-molecule-rotation-exciting-microwave signal. You perceive the sound only within a pinpoint-directed beam, at potentially enormous intensity. Spooky!

-- Cheers, -- Mr. d.