Answer:
a. approximately (first minimum.)
b. approximately (first maximum.)
c. approximately (second minimum.)
d. approximately (second maximum.)
Explanation:
Let represent the separation between the two speakers (the two "slits" based on the assumptions.)
Let represent the angle between:
- the line joining the microphone and the center of the two speakers, and
- the line that goes through the center of the two speakers that is also normal to the line joining the two speakers.
The distance between the microphone and point would thus be
meters.
Based on the assumptions and the equation from Young's double-slit experiment:
.
Hence:
.
The "path difference" in these two equations refers to the difference between the distances between the microphone and each of the two speakers. Let denote the wavelength of this wave.
.
Calculate the wavelength of this wave based on its frequency and its velocity:
.
Calculate for each of these path differences:
.
In each of these case, the distance between the microphone and would be
. Therefore:
- At the first minimum, the distance from
is approximately
.
- At the first maximum, the distance from
.
- At the second minimum, the distance from
.
- At the second maximum, the distance from
.