Question

Two small forward-facing speakers are 2.50 m apart. They are both emitting, in phase with each other, a sound of frequency 1100 Hz in a room where the speed of sound is 344 m/s. A woman is standing opposite the midpoint between the speakers and is initially 35.0 m from the midpoint. As she slowly walks parallel to the line connecting the speakers, at what angle θ (relative to the centerline coming outward from the midpoint between the speakers) will she first hear no sound?

Answer 1

There is an interference phenomenon (for acoustic waves) appearing in the room.

The condition for obtaining a minimum on the "observation screen" (the woman's ear) is:

k=an integer

The wavelength:

The small angle approximation [] cannot be used because the distances are too large.

The first minimum corresponds to k=0:

The next minimum is obtained for:

etc...

The woman is at an angle:

[Suppose she's coming from a larger angle than that corresponding to the first minimum/maximum.]

FROM NOW ON:

- I don't understand what 35 m represents: is it delta(y)? Is it L? From the text is not very clear, and also no figure is provided.

What I can do:

With theta(w) determined from eq.(1), replace it in eq.(2) and find k. It will be, probably, not an integer. The angle that the problem asks about is that corresponding to the first k integer smaller than k obtained from eq.(2).

So, take that k, replace in eq.(2) and find the angle.