Two speakers are placed side by side and driven by the same frequency of 0.50 kHz.If the distance from a person to one speaker is 5.0 m and the person detects little or no sound,which of the following is a possible the distance from the person to the other speaker? The sound speed in the room is 340 m/s.
A)7.7 m
B)8.1 m
C)8.4 m
D)9.1 m

Question

Quizplus · Accepted Answer

The phenomenon described is due to destructive interference, which occurs when two sound waves are out of phase by half a wavelength ($\lambda/2$). The path difference between the two speakers to the person's location must be an odd multiple of $\lambda/2$ for destructive interference to occur. Given the frequency $f = 0.50 \, \text{kHz}$ and the speed of sound $v = 340 \, \text{m/s}$, the wavelength $\lambda = v/f = 340/500 = 0.68 \, \text{m}$. For the first minimum (destructive interference), the path difference should be $\lambda/2 = 0.34 \, \text{m}$. However, since the person detects little or no sound, we are likely dealing with a higher order of destructive interference, where the path difference is an odd multiple of $\lambda/2$. The closest distance that would result in such a condition, given one path is 5.0 m, is found by calculating the possible distances and comparing them to the options. The correct answer, 8.1 m, implies a path difference that fits the criteria for destructive interference based on the given conditions.

Two Speakers Are Placed Side by Side and Driven by the Same