Answer:
f = 632 Hz
Explanation:
As we know that for destructive interference the path difference from two loud speakers must be equal to the odd multiple of half of the wavelength
here we know that
[tex]\Delta x = (2n + 1)\frac{\lambda}{2}[/tex]
given that path difference from two loud speakers is given as
[tex]\Delta x = 5.80 m - 3.90 m[/tex]
[tex]\Delta x = 1.90 m[/tex]
now we know that it will have fourth lowest frequency at which destructive interference will occurs
so here we have
[tex]\Delta x = 1.90 = \frac{7\lambda}{2}[/tex]
[tex]\lambda = \frac{2 \times 1.90}{7}[/tex]
[tex]\lambda = 0.54 m[/tex]
now for frequency we know that
[tex]f = \frac{v}{\lambda}[/tex]
[tex]f = \frac{343}{0.54} = 632 Hz[/tex]
