Suppose that the separation between two speakers A and B is 4.30 m and the speakers are vibrating in-phase. They are playing identical 103-Hz tones and the speed of sound is 343 m/s. An observer is seated at a position directly facing speaker B in such a way that his line of sight extending to B is perpendicular to the imaginary line between A and B. What is the largest possible distance between speaker B and the observer, such that he observes destructive interference

The largest  possible distance is

Explanation:

From the question we are told that

    The distance of  separation is  

      The  frequency of the tone played by both speakers is

     The speed of sound is  

The  wavelength of the tone played by the speaker is  mathematically evaluated as

substituting values

Let the the position of the observer be O

Given that the line of sight between observer and speaker B is  perpendicular to the distance between A and B then

        The distance between A and the observer is  mathematically evaluated using Pythagoras theorem as follows

Where x is the distance between the observer and B

  For the observer to observe destructive interference

So  

substituting values              

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wavelength divides in half and speed stays the same.