Answer:
The minimum distance is [tex]y = 892.48 \ cm[/tex]
Explanation:
The diagram of this set up is shown on the first uploaded image
From the question we are told that
The wavelength is [tex]\lambda = 9.00\ cm[/tex]
The width of the slit is [tex]d = 12.0 cm[/tex]
The distance of the microphone is [tex]L = 8.0 \ m = 8*100 = 800 \ cm[/tex]
Generally the diffraction minima in a single slit is mathematically represented as
[tex]dsin \theta = m \lambda[/tex]
Where m is the order of diffraction which is 1 in this question
So making [tex]\theta[/tex] the subject
[tex]\theta = sin^{-1} [\frac{m * \lambda }{ d} ][/tex]
[tex]\theta = sin^{-1} [\frac{1 * 9.00}{12.00} ][/tex]
[tex]\theta =0.84 \ rad[/tex]
Now from the diagram
[tex]y = 800 tan 0.84[/tex]
[tex]y = 800* (1.1156)[/tex]
[tex]y = 892.48 \ cm[/tex]
