Does Geometry Influence Sound Propagation?

[amd123]

Homework Statement

Two recording devices are set 2400 feet apart, with the device at Point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?

Homework Equations

I have no clue.

The Attempt at a Solution

I've tried drawing a diagram and setting up an equation like this:
(x^2/(400^2))-(y^2/800sqrt(2))=1

now I have no idea if that is right or what to do after that.

 

[Mark44]

Homework Statement

Two recording devices are set 2400 feet apart, with the device at Point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?

Homework Equations

I have no clue.

How about the formula for a hyperbola, and the relationship between a, b, and c in the formula?

The Attempt at a Solution

I've tried drawing a diagram and setting up an equation like this:
(x^2/(400^2))-(y^2/800sqrt(2))=1

now I have no idea if that is right or what to do after that.

 

[amd123]

i know the hyperbola equation
and that c^2 = a^2 + b^2

 

[Mark44]

And what are a, b, and c in your hyperbola? Where are the foci in your hyperbola? Where are the vertices in your hyperbola?

A property of hyperbolas that is important in this problem is that if P(x, y) is a point on the hyperbola, and if F₁ and F₂ are its two foci, then PF₁ - PF₁ equals a constant.

 

[amd123]

Im guessing that c = the distance between A and B.
a = the difference in time that the sound reaches the points
b = what I need to find?

I'm still unsure at how I'm reaching this conclusion, my book just says this is true and doesn't explain why.

 

[Mark44]

Im guessing that c = the distance between A and B.
a = the difference in time that the sound reaches the points
b = what I need to find?

I'm still unsure at how I'm reaching this conclusion, my book just says this is true and doesn't explain why.

Your book should provide some discussion of hyperbolas, including their equations and what a, b, and c mean. Here is a link to some other information - http://en.wikipedia.org/wiki/Hyperbola.