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,
$$m_1=m_2=3.2kg$$
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:
$$v=\sqrt{\frac{(3.2\times 10)}{0.008}}$$ 
$$=\sqrt{\frac{(32\times {10}^3)}{8}}$$ 

$$=2\times 10\sqrt{10}$$ 

$$=20\times 3.14\approx 63\text{ s }$$
For string AB,
$$T=2\times 3.2g=64N$$ 
Thus, we  have:
$$v=\sqrt{\left(\frac{T}{m}\right)}$$ 
$$=\sqrt{\left(\frac{64}{0.01}\right)}=\sqrt{6400}$$
$$=80\text{ m/s }$$