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.

• A. $\text{ i. }\theta =10.2^{\circ },20.5^{\circ },30.8^{\circ },41.1^{\circ },51.4^{\circ },\text{ ii. Yes, the student is standing at an angle of destructive interference. }$
• B. $\text{ i. }\theta =5.0^{\circ },15.0^{\circ },25.0^{\circ },35.0^{\circ },45.0^{\circ },\ \text{ii.}\text{ Yes, the student is standing at an angle of destructive interference. }$
• C. $\text{ i. }\theta =6.15^{\circ },18.7^{\circ },32.4^{\circ },48.6^{\circ },74.6^{\circ },\ \text{ii.}\text{ No, the student is not standing at an angle of destructive interference. }$
• D. $\text{ i. }\theta =7.5^{\circ },22.5^{\circ },52.5^{\circ },67.5^{\circ },74.6^{\circ },\ \text{ ii.}\text{ No, the student is not standing at an angle of destructive interference. }$

Answer: (C)