The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is
A) $\pi$ radians.
B) $\pi$/2 radians.
C) $\pi$/4 radians.
D) $\pi$/8 radians.
E) $\pi$/16 radians.

Question

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is
A) $\pi$ radians. 
B) $\pi$/2 radians. 
C) $\pi$/4 radians. 
D) $\pi$/8 radians. 
E) $\pi$/16 radians.

Quizplus · Accepted Answer

To find the phase difference between two waves, we need to compare the difference between the two waves at the same point in space and time. Looking at the figure, we can see that the two waves have the same amplitude and wavelength, but they are shifted in phase by half a wavelength. Therefore, the phase difference between them is half of the wavelength, which is given by:
(phase difference) = (wavele​ngth)/2 = π/2
Since the wavelength is given as λ = 2π/k, where k is the wave number, we have:
(phase difference) = π/2 = π/2k
Solving for k, we get:
k = 2/π
Substituting this value of k in the wavelength expression, we get:
λ = 2π/k = π
Therefore, the two waves have a phase difference of half a wavelength or π/2 radians, which corresponds to choice B.

The Figure Shows Two Waves Traveling in the Positive-X Direction π\piπ

The Figure Shows Two Waves Traveling in the Positive-X Direction $\pi$