Answer:
The value is [tex]\lambda = 2 \ m[/tex]
Explanation:
From the question we are told that
The distance of the speaker from the second speaker to the east is [tex]d = 3 \ m[/tex]
The distance of the speaker from the listener to the south is [tex]a = 4 \ m[/tex]
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
[tex]y = \frac{\lambda}{2}[/tex]
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
[tex]b = \sqrt{d^ 2 + a^2 }[/tex]
=> [tex]b = \sqrt{3^ 2 + 4^2 }[/tex]
=> [tex]b = 5[/tex]
Generally the path difference between the two speaker with respect to the listener is
[tex]y = b - a[/tex]
=> [tex]y = 5 - 4[/tex]
=> [tex]y = 1[/tex]
So
[tex]1 = \frac{\lambda}{2}[/tex]
=> [tex]\lambda = 2 \ m[/tex]
