Question
Question: Two pulses on a string approach each other at speeds of 1 m/s. What is the shape of the string at t=...
Two pulses on a string approach each other at speeds of 1 m/s. What is the shape of the string at t=6s?
A
(A)
B
(C)
C
(B)
D
(D)
Answer
(A), (B)
Explanation
Solution
The two triangular pulses, each with a base width of 4m and traveling at 1 m/s, move towards each other. After 6 seconds, each pulse travels a distance of 6m. The left pulse shifts from [0, 4] to [6, 10], with its peak moving from x=2 to x=8. The right pulse shifts from [16, 20] to [10, 14], with its peak moving from x=18 to x=12. At t=6s, the pulses meet at x=10, where both have zero amplitude. The resulting shape is the concatenation of these two displaced triangles, forming two adjacent peaks.