A music practice room has an entrance consisting of two doorways, each 1.1 m wide and separated by a distance of 3.1 m. Outside the practice room, a tuning fork is struck in the hallway, producing a sound wave with a frequency of 512 Hz.
(i) Find all the angles of θ at which no sound will be heard within the practice room when the tuning fork is struck.
(ii) If a student is standing inside of the practice room as illustrated below when the tuning fork is struck outside of the room, will the student have a good explanation for not hearing the sound? Explain.
Assuming that the speed of sound is 340 m/s and that it has not bounced off the walls inside of the room.

$\(\text{ i. }\]\theta\) =10.2^{\(\circ\) },20.5^{\(\circ\) },30.8^{\(\circ\) },41.1^{\(\circ\) },51.4^{\(\circ\) },\(\text{ ii. Yes, the student is standing at an angle of destructive interference. }\)$

$\(\text{ i. }\[\theta\) =5.0^{\(\circ\) },15.0^{\(\circ\) },25.0^{\(\circ\) },35.0^{\(\circ\) },45.0^{\(\circ\) },\ \(\text{ii.}\]\text{ Yes, the student is standing at an angle of destructive interference. }\)$

$\(\text{ i. }\[\theta\) =6.15^{\(\circ\) },18.7^{\(\circ\) },32.4^{\(\circ\) },48.6^{\(\circ\) },74.6^{\(\circ\) },\ \(\text{ii.}\]\text{ No, the student is not standing at an angle of destructive interference. }\)$

$\(\text{ i. }\[\theta\) =7.5^{\(\circ\) },22.5^{\(\circ\) },52.5^{\(\circ\) },67.5^{\(\circ\) },74.6^{\(\circ\) },\ \(\text{ ii.}\]\text{ No, the student is not standing at an angle of destructive interference. }\)$