Two small loudspeakers that are 5.50 apart are emitting sound in phase. From both of them, you hear a singer singing C# (frequency 277 ), while the speed of sound in the room is 340 . Assuming that you are rather far from these speakers, if you start out at point equidistant from both of them and walk around the room in front of them, at what angles (measured relative to the line from to the midpoint between the speakers) will you hear the sound:

Question

Two small loudspeakers that are 5.50 apart are emitting sound in phase. From both of them, you hear a singer singing C# (frequency 277 ), while the speed of sound in the room is 340 . Assuming that you are rather far from these speakers, if you start out at point equidistant from both of them and walk around the room in front of them, at what angles (measured relative to the line from to the midpoint between the speakers) will you hear the sound:

A)maximally enhanced? Neglect any reflections from the walls.
Type absolute values of all possible angles in increasing order separating them with commas.
A=??? in degrees

B)cancelled? Neglect any reflections from the walls.
Type absolute values of all possible angles in increasing order separating them with commas.
B=??? in degrees

Answer 1

You need to find distance from each speaker from the midpoint as a function of the angle.

Then set the difference of distances equal to for a, multiples of wavelength of 277hz, and for b, multiples of half wavelengths.

I would recommend use the law of cosines.

Your known will be the base side (5.5/2 m), theta, and some distance on the radial from midpoint of the speakers to the chosen point, so you know SAS