Two blocks each having a mass of 3.2 kg are connected by a wire CD and the system is suspended from the ceiling by another wire AB as shown in the figure. The linear mass density of the wire AB is 10 g/m and that of CD is 8 g/m. Find the speed of a transverse wave pulse produced in AB and in CD.

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Solution

$m_{1} = m_{2} = 3.2 k g$
mass per unit length of $A B = 10 g / m t = 0.01 k g . m t$
mass per unit length of $C D = 8 g / m t = 0.008 k g / m t$
for the string $C D, T = 3.2 \times g$
$\Rightarrow v = \sqrt{(T / m)} = \sqrt{(3.2 \times 10) / 0.008} = \sqrt{(32 \times 10^{3}) / 8} = 2 \times 10 \sqrt{10} = 20 \times 3.14 = 63 m / s$
for the string $A B, T = 2 \times 3.2 g = 6.4 \times g = 64 N$
$\Rightarrow v = \sqrt{(T / m)} = \sqrt{(64 / 0.01)} = \sqrt{6400} = 80 m / s$

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