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Three pieces of string, each of length \( L \), are joined together end-to-end, to make a combined string of length \( 3 L \). The first piece of string has mass per unit length \( \mu_{1} \), the second piece has mass per unit length \( \mu_{2}=4 \mu_{1} \) and the third piece has mass per unit length \( \mu_{3}=\mu_{1} / 4 \).
(a) If the combined string is under tension \( F \), how much time does it take a transverse wave to travel the entire length \( 3 L \) ? Give your answer in terms of \( L, F \) and \( \mu_{1} \).
(b) Does your answer to part (a) depend on the order in which the three piece are joined together? Explain.
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