Parabolic reflectors with microphon located at the focus are used to capture sounds from a...
Parabolic reflectors with microphon located at the focus are used to capture sounds from a distance. The sound waves enter the reflector and are concentrated toward the microphone. How far from the reflector should a microphone be placed if the reflector has a width of 3 feet and a depth of 1.25 feet?
Answer & Explanation
The parabola is horizontal so the standard form is:
Since the vertex is at (h, k) and the focus is at (h +p, k), then the microphone must be placed |p feet to the right of the vertex. If the vertex is at (0,0), then h = 0 and k = 0:
To find p, substitute a point. A point on the parabola is (1.25, 1.5) since the depth is 1.25 ft and the width is 3 m (half of it).
So, the microphone should be placed 0.45 ft to the right of the vertex of the reflector.
0.45 ft to the right of the vertex of the reflector