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Two identical loudspeakers 2.20 m apart are emitting sound waves into a room where the speed...

Two identical loudspeakers 2.20 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 4.00 m in front of one of the speakers, perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound.

What is the lowest possible frequency of sound for which this is possible?

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Answer #1

The distance of the observer from the 1st source is
   
And as the distance between the two sources is d = 4.0 m, so, the distance between the observer and the 2nd source is
   
And so, the path difference is
  
And the condition for constructive interference is
   
where, n = 1, 2, 3, 4, ......, integers.
where, c is the speed of the sound in the air and f is the frequency of the wave.
And so, the frequency is
   
And so, the lowest frequency is for n = 1, and the numerical value of this is given by
  
  

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