Question

Parabolic microphones are used for field audio during sports events. The microphones are manufactured such that the equation of their cross section is x=1/34y^2, in inches. The feedhorn part of the microphone is located at the focus

a. How far is the feedhorn from the edge of the parabolic surface of the microphone?

b. What is the diameter of the microphone? Explain your reasoning

c. If the diameter is increased by 5 inches, what is the new equation of the cross section of the microphone?​

Answer 1

a. 8.5 in.

b. 34 in

c. x = 1/39 x^2.

Explanation:

Part a.

x = 1/34 y^2

y^2 = 34x

Comparing with y^2 = 4px where p is the focus:

4p = 34

p = 8.5 in.

Part b.

The diameter = 4p = 34 in.

Part c.

Diameter = 4p = 34 + 5 = 39 in

The new equation is x = 1/39 x^2.