Find the distance between objects and sound source

[jamiewilliams]

Homework Statement

One microphone is located at the origin, and a second microphone is located on the +y-axis. The microphones are separated by a distance of D= 1.21m. A source of sound is located on the +x-axis, its distance from microphones 1 and 2 being L1 and L2, respectively. The speed of sound is 342 m/s. The sound reaches microphone 1 first, and then 1.67 ms later it reaches microphone 2. Find the distances (in m) of L1 and L2.

Homework Equations

x=vΔt

The Attempt at a Solution

First I converted 1.67 ms to .00167 s. I know that vΔt=the extra distance sound must travel to reach mic 2 (.57114 m) and I know that the sound source and two lengths create a right triangle, but I am stuck on how to get the length of L1.

 

[Nugatory]

You have two unknowns, L1 and L2.

You know that D, L1, and L2 form a right triangle. That will give you one equation with the two unknowns.

You've already found the extra distance, and that tells you something about the relationship between L1 and L2 which you can use to write a second equation in the two unknowns.

You should be able to take it from there with a bit of algebra.

 

[jamiewilliams]

You've already found the extra distance, and that tells you something about the relationship between L1 and L2 which you can use to write a second equation in the two unknowns.

You should be able to take it from there with a bit of algebra.

I have L1^2 + (1.21)^2 = (L1 + .57114)^2 and I can't seem to move the algebra around to get the right answer for L1.

I know that (from the book) L1= .996m and L2= 1.57m, but I never arrive at the right answer. Am I missing a step or just getting the algebra wrong?