A standing wave is shown in the figure on the right. If the period of the wave is T, the shortest time it takes for the wave to go from the solid curve to the dashed curve is
A) T/4.
B) T/3.
C) T/2.
D) 3T/4.
E) None of these is correct.

Question

A standing wave is shown in the figure on the right. If the period of the wave is T, the shortest time it takes for the wave to go from the solid curve to the dashed curve is
A) T/4. 
B) T/3. 
C) T/2. 
D) 3T/4. 
E) None of these is correct.

Quizplus · Accepted Answer

The shortest time it takes for the wave to go from the solid curve to the dashed curve corresponds to one-quarter of a wavelength, which for a standing wave is half of the distance between two consecutive nodes. Since the wave is traveling at a constant speed (assuming a uniform medium), the time it takes to travel half a wavelength is half the period:

t = T/2

Therefore, the shortest time it takes for the wave to go from the solid curve to the dashed curve is T/2 divided by 2, which is T/4. Thus, (A) is incorrect. Similarly, the other answer choices are also incorrect. Therefore, the best choice is (C).

A Standing Wave Is Shown in the Figure on the Right