Answer: [tex]278\ Hz[/tex]
Explanation:
Given
Distance between two speakers is 8 m
Man is standing 12 away from the wall
When the person moves 3 parallel to the wall
the parallel distances from the speaker become 4+3, 4-3
Now, the difference of distances from the speaker is
[tex]\Delta d=\sqrt{12^2+(4+3)^2}-\sqrt{12^2-(4-3)^2}\\\Delta d=1.85\ m[/tex]
Condition for destructive interference is
[tex]\Delta d=(2n-1)\dfrac{\lambda }{2}=(2n-1)\dfrac{\nu }{2f}\\\\\Rightarrow f=(2n-1)\dfrac{v}{2\Delta d}[/tex]
for second destructive interference; n=2
[tex]\Rightarrow f=(2\times 2-1)\dfrac{343}{2\times 1.85}=278.10\approx 278\ Hz[/tex]
