Question

One small speaker is placed 3m to the east of a second speaker, and a listener stands 4m directly south of one of the speakers. That listener finds that if they move in any direction, the sound gets louder. What is the longest possible wavelength of the sound from the speakers

Answer 1

Answer:

The value is $\lambda = 2 \ m$

Explanation:

From the question we are told that

     The distance of the speaker  from the  second speaker  to the east is  $d = 3 \ m$

      The distance of the speaker  from the listener  to the south is     $a = 4 \ m$

Generally given that if the speaker move in any direction, their sound become  louder , it then mean that the position of the listener of minimum sound (i.e a position of minima ) ,

Generally the path difference of the sound produce by both speaker at a position of minima is mathematically represented as

              $y = \frac{\lambda}{2}$

Generally considering the orientation  of the speakers and applying Pythagoras theorem we see that  distance from the second speaker to the listener  is mathematically represented as

             $b = \sqrt{d^ 2 + a^2 }$

=>           $b = \sqrt{3^ 2 + 4^2 }$

=>           $b = 5$

Generally the path difference between the two speaker with respect to the  listener is  

              $y = b - a$

=>           $y = 5 - 4$

=>           $y = 1$

So  

              $1 = \frac{\lambda}{2}$

=>           $\lambda = 2 \ m$