As a wave moves to the right in an elastic rope, a sequence of pictures (1 through 6) is taken at intervals of one second. An arrow points out a particle that is attached to the rope. If the width of the picture is 8 cm, this wave has a period of
A) 0.2 s
B) 10 s
C) 3 s
D) 6 s
E) 12 s

Question

As a wave moves to the right in an elastic rope, a sequence of pictures (1 through 6) is taken at intervals of one second. An arrow points out a particle that is attached to the rope. If the width of the picture is 8 cm, this wave has a period of 
A) 0.2 s 
B) 10 s 
C) 3 s 
D) 6 s 
E) 12 s

Quizplus · Accepted Answer

From the sequence of pictures, we can see that it takes 6 pictures for the wave to complete one full wavelength. Since each picture is taken at intervals of one second, the time for the wave to complete one wavelength is 6 seconds. Therefore, the period of the wave (time for one complete cycle) is twice the time for the wave to complete one wavelength, which is 2 x 6 = 12 seconds. However, the width of the picture is only 8 cm, which means one wavelength is equivalent to the width of the picture. Therefore, the period of the wave is 12 seconds per wavelength. To find the period of the wave with a length of 1 cm, we divide 12 seconds by 8 cm, which gives us 1.5 seconds per centimeter. Finally, we can find the period of the wave with a length of 1 meter by multiplying the period of the wave with a length of 1 cm by 100, which gives us 150 seconds or 2.5 minutes. Therefore, the answer is B) 10 s, which is the closest choice to 12 seconds, the period of the wave per wavelength.

As a Wave Moves to the Right in an Elastic