The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is
A) 2.0 mm.
B) 1.8 mm.
C) 1.4 mm.
D) 1.0 mm.
E) 0.83 mm.

Question

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is
A) 2.0 mm. 
B) 1.8 mm. 
C) 1.4 mm. 
D) 1.0 mm. 
E) 0.83 mm.

Quizplus · Accepted Answer

The amplitude of the resultant wave can be found by adding the amplitudes of the individual waves at each point along the x-axis. At x=0 mm, the amplitude of wave 1 is 1.2 mm and the amplitude of wave 2 is -0.6 mm (since wave 2 is inverted). Therefore, the amplitude of the resultant wave is 1.2 mm - 0.6 mm = 0.6 mm. At x=4 mm, the amplitude of wave 1 is -1.0 mm and the amplitude of wave 2 is 0.8 mm. Therefore, the amplitude of the resultant wave is -1.0 mm + 0.8 mm = -0.2 mm. Finally, at x=8 mm, the amplitude of wave 1 is 0.8 mm and the amplitude of wave 2 is -0.6 mm. Therefore, the amplitude of the resultant wave is 0.8 mm - 0.6 mm = 0.2 mm. The maximum amplitude occurs at x=2 mm, where the amplitude of wave 1 is 0.4 mm and the amplitude of wave 2 is 1.0 mm. Therefore, the amplitude of the resultant wave is 0.4 mm + 1.0 mm = 1.4 mm. Therefore, the best choice is C) 1.4 mm.

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