As the drawing shows, one microphone is located at the origin, and a second micr

Question

As the drawing shows, 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 = 1.50 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 343 m/s. The sound reaches microphone 1 first, and then, 1.46 ms later, it reaches microphone 2. Find the distance L1 and L2.

Picture: microphone 1 at origin. microphone 2 on +y axis 1.50 m above it. sound source is on +x axis a distance L1 from origin. sound source is distance "l2" from microphone 2.

Explanation / Answer

L1=2.5593m, L2=3.067m Set up a right triangle on the x,y system where: y=1.69m, x=L1, and the diagonal = L2=L1+(343 * .00148) L2 = X+.50764m Using Pythagorean, 169^2 + x^2 = (x+.50764)^2 Solve for x, and find x = 2.5593 = L1 Adding the .50764m to L1 gives L2 = 3.067m

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