Halliday, Resnick & Walker — Waves-I: Problem 36

36 In Fig. 16-32a, string 1 has a linear density of $3.00 \text{ g/m}$, and string 2 has a linear density of $5.00 \text{ g/m}$. They are under tension due to the hanging block of mass $M = 800 \text{ g}$. Calculate the wave speed on (a) string 1 and (b) string 2. (Hint: When a string loops halfway around a pulley, it pulls on the pulley with a net force that is twice the tension in the string.) Next the block is divided into two blocks (with $M_1 + M_2 = M$) and the apparatus is rearranged as shown in Fig. 16-32b. Find (c) $M_1$ and (d) $M_2$ such that the wave speeds in the two strings are equal.