Solve the Problem $\frac { x ^ { 2 } } { 330 ^ { 2 } } - \frac { y ^ { 2 } } { 1,361 ^ { 2 } } = 1$

question 109

Multiple Choice

Solve the problem.
-Suppose that two microphones 2,800 m apart at points A = (1,400, 0) and B = (-1,400, 0) detect the sound of a rifle shot. The time difference between the sound detected at A and the sound detected at B is 2 sec. If sound travels at approximately 330 m/sec, find an equation of the hyperbola with foci
At A and B defining the points where the shooter may be located.

• A) \(\frac { x ^ { 2 } } { 330 ^ { 2 } } - \frac { y ^ { 2 } } { 1,361 ^ { 2 } } = 1\)
• B) \(\frac { x ^ { 2 } } { 1,400 ^ { 2 } } - \frac { y ^ { 2 } } { 330 ^ { 2 } } = 1\)
• C) \(\frac { x ^ { 2 } } { 2,800 ^ { 2 } } - \frac { y ^ { 2 } } { 2,721 ^ { 2 } } = 1\)
• D) \(\frac { y ^ { 2 } } { 1,361 ^ { 2 } } - \frac { x ^ { 2 } } { 330 ^ { 2 } } = 1\)

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Definitions:

Scala Tympani

A coiled, fluid-filled tube within the inner ear, part of the cochlea, that transmits sound vibrations to the auditory nerve.

Basilar Membrane

A structure in the cochlea of the inner ear that plays a key role in the sense of hearing by vibrating in response to sound.

Tectorial Membrane

A structure located within the spine that provides stability by connecting the atlas to the axis, which are the first two cervical vertebrae.

Auditory Ossicles

The small bones in the middle ear (the malleus, incus, and stapes) that transmit sound vibrations from the ear drum to the inner ear.