Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians?
A) x = 0, 1.0 m, 2.0 m
B) x = 0.50 m, 1.5 m
C) x = 0.50 m, 1.0 m, 1.5 m
D) x = 0.75 m, 1.25 m
E) x = 0.25 m, 0.75 m, 1.25 m, 1.75 m

Question

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians? 
A) x = 0, 1.0 m, 2.0 m 
B) x = 0.50 m, 1.5 m 
C) x = 0.50 m, 1.0 m, 1.5 m 
D) x = 0.75 m, 1.25 m 
E) x = 0.25 m, 0.75 m, 1.25 m, 1.75 m

Quizplus · Accepted Answer

The path difference between the two sources for waves to be out of phase by $\pi$ radians is half the wavelength, or 0.5 m. This occurs when the waves from one source are at the crest while the other is at the trough. 
The midpoint between the two sources is at 1.0 m. Therefore, the waves will be out of phase by $\pi$ radians at equal distances on either side of the midpoint, which are at 0.75 m and 1.25 m. Hence, the correct answer is D).

Two Point Sources Emit Sound Waves of 1