Please I need help with my physics homework!! I'd be so grateful if you could include workings also, but if not don't worry!!?

Question

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 = 1.52 m. A source of sound is located on the +x axis, its distances 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, 1.24 ms later, it reaches microphone 2. Find the distances (in m) (a) L1 and (b) L2

az_lender · Answer

The difference L2 - L1 must be (342 m/s)(0.00124 s) = 0.424 m or 42.4 cm.

So we have a right triangle with vertical leg 1.52m, but the hypotenuse is only 0.424m longer than the horizontal leg, so:
(L1)^2 + (L1 + 42.4)^2 = 152^2,
where the lengths are now in cm.
2(L1)^2 + (84.8)L1 - 21306.24 = 0.
Use the quadratic formula and choose the positive solution !

billrussell42 · Answer

let t₁ be time to reach mike 1
L₁/t₁ = 342
and for 2
L₂/t₂ = 342
and
t₂–t₁ = 0.00142 s

from the geometry
L₁² + 1.52² = L₂²
L₂ = √(L₁² + 1.52²)

4 equations, 4 unknowns, possibly solvable.
but I don't see any easy solution.

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Please I need help with my physics homework!! I'd be so grateful if you could include workings also, but if not don't worry!!?

2 Answers