Question

Diffraction occurs for all types of waves, including sound waves. High-frequency sound from a distant source with wavelength 9.00 cm passes through a slit 12.0 cm wide. A microphone is placed 8.00 m directly in front of the center of the slit, corresponding to point O in Fig. 36.5a. The microphone is then moved in a direction perpendicular to the line from the center of the slit to point OAt what minimal distance from O will the intensity detected by the microphone be zero?

Answer 1

Answer:

The minimum  distance is  $y = 892.48 \ cm$

Explanation:

The diagram of this set up is shown on the first uploaded image

From the question we are told that

    The  wavelength is $\lambda = 9.00\ cm$

     The width of the slit is  $d = 12.0 cm$

     The distance of the microphone is  $L = 8.0 \ m = 8*100 = 800 \ cm$

Generally the diffraction minima in a single slit is mathematically represented as

    $dsin \theta = m \lambda$            

 Where m is the order of diffraction which is  1  in this question

   So  making $\theta$ the subject

           $\theta = sin^{-1} [\frac{m * \lambda }{ d} ]$

             $\theta = sin^{-1} [\frac{1 * 9.00}{12.00} ]$

            $\theta =0.84 \ rad$

   Now from the diagram

              $y = 800 tan 0.84$

             $y = 800* (1.1156)$

             $y = 892.48 \ cm$