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 (figure 15-E5). 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.
Figure

Answer 1

Transverse Wave pulse is 30 $ms^-^1$

Explanation:

Given, $m_1 = m_2$= 3.2 kg

Linear Mass Density of wire AB = $10\ gm^-^1 = 0.001\ kgm^-^1$

Linear Mass Density of wire CD = $8\ gm^-^1 = 0.008\ kgm^-^1$

For String CD, velocity can be defined as

v = $\sqrt (\frac {T}{m})$

Here, T is tension and m is mass per unit length  

For String CD,

T = $3.2 \times g$

Hence, we have  

v = $\sqrt (\frac {3.2 \times 10}{0.008})$

= $\sqrt (\frac {32 \times 10^3}{8})$

= $2 \times 10\sqrt 10$

= $20 \times 3.14$ = 63 s

For String AB,

T = $2 \times 3.2$ g = 64 N

Thus we have

v = $\sqrt (\frac {T}{m})$

= $\sqrt (\frac {64}{0.01})$

= $\sqrt 6400$

= $80 ms^-^1$