Two speakers are placed side by side and driven by the same frequency of 500 Hz. If the distance from a person to one speaker is 5.00 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 is 340 m/s.)

a) 8.4 m
b) 9.1 m
c) 8.1 m
d) 7.7 m

The correct option is option "a" i.e.  8.4 m

Explanation:

Frequency (f) = 500 Hz

speed of sound (v) = 340 m/s

wavelength =  

                    =

                    = 0.68 meters

Half wavelength = wavelength

                           = 0.34 meters

For the sound interference to be destructive, the second source must be an odd multiple of 1/2 wavelength away from the first.  so:

5 m + 0.34 m = 5.34 m

5 m + 3×0.34 m = 6.02 m

5 m + 5×0.34 m = 6.7 m

5 m + 7×0.34 m = 7.38 m

5 m + 9×0.34 m = 8.06 m  

5 m + 11×0.34 m = 8.74 m

The value closest to any options provided above is 8.06 m. So the correct option is 8.4 m.