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 soundreaches 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" frommicrophone 2.

Answer 1

(L2-L1)=0.00161*343 =0.55....(1)

By Pythagorean Theorem,
L12+1.52=L22 ....(2)

By (1), L2= L1+ 0.55
By (2), L1^2 + 1.5^2 = (L1+0.55)^2
-->L1^2 + 2.25 = L1^2+ 1.1 L1 + 0.3025
--> 1.1L1= 2.25 -0.3025 =1.9475
--> L1= 1.9475 /1.1 =1.77m

L2= 1.77+0.55= 2.32 m