Two sound speakers located at different points S1 and S2 are in-phase emitting a sound of frequency 494 Hz tra

Two sound speakers located at different points S1 and S2 are in-phase emitting a sound of frequency 494 Hz travelling in air.

Six observers at points A, B, C, D, E, and F are listening to the sound created by the superposition of the two waves.

The listing below indicates the distance from each observer to speakers S1 and S2.

For example, D-S2 = 1.23 m will indicate that the observer at D is at a distance of 1.23 m from the speaker at S2.

Which of the observers will listen to no sound on account of destructive interference?

Choose which one is the correct answer from the list below and why.
A) E-S1 = 170 cm and E-S2 = 308 cm
B) B-S1 = 210 cm and B-S2 = 279 m
C) D-S1 = 279 cm and D-S2 = 210 cm
D) A-S1 = 210 cm and A-S2 = 244 m


Please explain your answer. Thanks!

Assuming a sound speed of 343m/sec.,:
Wavelength of 494Hz = (343/494) = 0.69433 metres.
For destructive interference, the path length difference between observers must be 1/2 wavelength or an odd 1/2 wavelength which = 0.347m (34.7cm).
Difference in paths A is (308 - 170) = 138cm. (138/34.7) = no good.
Difference in paths B is (279 - 210) = 69cm. (69/34.8) = no good.
Difference in paths C is the same as difference in paths B, = no good.
Difference in paths D is (244 - 210) = 34cm. So this one is good!

Answer is D. It's the closest for my assumed speed for sound. Your given speed might be nearer 337m/sec.