Two speakers are located in a line and pointed at you playing 80 Hz tones. The s

Question

Two speakers are located in a line and pointed at you playing 80 Hz tones. The speakers are not synchronized in time or space. One speaker is located a distance of L_1 = 8.0 m from you and the other is located a distance L_2 that varies. As the location of L_2 changes you hear the sound intensity alternating between minimum and maximum levels. You notice that the closest that the two speakers can be for a minimum to occur is when L_2 = 9.36 m. What are two positions that L_2 can be moved closest to 9.36 m that produce maximums? The speed of sound in this problem is 340 m/s. What is the time delay At between the two speakers?

Explanation / Answer

a) minimum path diffrence for maximum, L2 - L1 = lamda/2

9.36 - 8 = lamda/2

==> lamda = 1.36*2

= 2.72 m

minimum path diffrence for maximum, L2 - L1 = 0

L2 = L1

= 8 m

second minimum path diffrence for maximum, L2 - L1 = lamda

L2 = L1 + lamda

= 8 + 2.72

= 10.72 m

b) when L1 = L2 = 8 m

there is no time delay.

when L1 = 8 m

L2 = 10.72 m

the time delay, delta_t = (L2 - L1)/v

= (10.72 - 8)/340

= 0.008 s or 8 ms

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