Two loudspeakers at an outdoor rock concert are located 3.3 meters apart. You ar

Question

Two loudspeakers at an outdoor rock concert are located 3.3 meters apart. You are standing 17.2 meters from one of the speakers and 20 from the other. During a sound check, the technician sends the exact same frequency to both speakers while you listen. The technician starts at 20Hz and slowly increases it to 30,000Hz.

What is the lowest frequency where you will hear a minimum signal ?

What is the second lowest frequency where you will hear a minimum signal ?

What is the lowest frequency where you will hear a maximum signal ?

What is the second lowest frequency where you will hear a maximum signal ?

Explanation / Answer

For minimum signal:

Path difference, x = (n + 0.5)c/f

=> frequency, f = (n + 0.5)c/x

Lowest frequency, fo = (0 + 0.5) * 340 / (20 - 17.2) = 60.7 Hz

Second lowest frequency, f1 = (1 + 0.5) * 340 / (20 - 17.2) = 182.1 Hz

For maximum signal:

Path difference, x = nc/f

=> frequency, f = nc/x

Lowest frequency, f1 = 1 * 340 / (20 - 17.2) = 121.4 Hz

Second lowest frequency, f2 = 2 * 340 / (20 - 17.2) = 243.9 Hz

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