Three pieces of string

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics

Problem

Three pieces of string, each of length LL, are joined end-to-end to make a combined string of length 3L3L. The first piece has mass per unit length μ1\mu_1, the second has mass per unit length μ2=4μ1\mu_2=4\mu_1, and the third has mass per unit length μ3=μ14\mu_3=\frac{\mu_1}{4}. (1) If the combined string is under tension FF, how much time does a transverse wave take to travel the entire length 3L3L? Give your answer in terms of LL, FF, and μ1\mu_1. (2) Does your answer to part (a) depend on the order in which the three pieces are joined together? Explain.

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