Question

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 (See following figure). The linear mass density of the wire AB is 10 g m⁻¹ and that of CD is 8 g m⁻¹. Find the speed of a transverse wave pulse produced in AB and CD.

Answer 1

Given,
\[m_1  =  m_2  = 3 . 2  kg\]
Linear mass density of wire AB = 10 gm⁻¹ = 0.01 kgm⁻¹
Linear mass density of wire CD = 8 gm⁻¹ = 0.008 kgm⁻¹
For string CD, velocity is defined as
\[v = \sqrt{\left( \frac{T}{m} \right)}\]
Here, T is the tension and m is the mass per unit length.
For string CD, 
\[T = 3 . 2 \times g\]
Thus, we have:
\[v   = \sqrt{\frac{\left( 3 . 2 \times 10 \right)}{0 . 008}}\] 
\[= \sqrt{\frac{\left( 32 \times {10}^3 \right)}{8}}\] 

\[= 2 \times 10\sqrt{10}\] 

\[= 20 \times 3 . 14 \approx 63  \text{ s }\]
For string AB,
\[T = 2 \times 3 . 2g = 64  N\] 
Thus, we  have:
\[v = \sqrt{\left( \frac{T}{m} \right)}\] 
\[= \sqrt{\left( \frac{64}{0 . 01} \right)} = \sqrt{6400}\]
\[= 80  \text{ m/s }\]