Three separate strings are made of the same material. String 1 has length L and tension $ \tau $, string 2 has length 2L and tension 2 $ \tau $ and string 3 has length 3L and tension 3 $ \tau $. A pulse is started at one end of each string. If the pulses start at the same time, the order in which they reach the other end is:
A) 1, 2, 3
B) 3, 2, 1
C) 2, 3, 1
D) 3, 1, 2
E) they all take the same time

Question

Three separate strings are made of the same material. String 1 has length L and tension  $ \tau $, string 2 has length 2L and tension 2 $ \tau $ and string 3 has length 3L and tension 3 $ \tau $. A pulse is started at one end of each string. If the pulses start at the same time, the order in which they reach the other end is:
A) 1, 2, 3
B) 3, 2, 1
C) 2, 3, 1
D) 3, 1, 2
E) they all take the same time

Quizplus · Accepted Answer

The speed of a wave on a string is given by v = sqrt(T/μ), where T is the tension and μ is the linear density. Since all three strings are made of the same material, they have the same linear density. Therefore, the speed of the wave on each string is proportional to the square root of the tension. Since string 1 has the lowest tension, it will have the lowest wave speed. String 2 has twice the tension of string 1, so it will have a wave speed that is sqrt(2) times faster than string 1. String 3 has three times the tension of string 1, so it will have a wave speed that is sqrt(3) times faster than string 1. Therefore, the order in which the pulses reach the other end is 1, 2, 3.

Three Separate Strings Are Made of the Same Material τ \tau τ

Three Separate Strings Are Made of the Same Material $\tau$