Question

Two blocks each having a mass of 3.2 kg are connected by awire 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 $10g{m}^{-1}$ and that of CD is $8g{m}^{-1}.$ Find the speed of a transverse wave pulse produced in AB and in CD.

Answer 1

$m_1=m_2=3.2kg$

Mass per unit length of AB

= 10 gm/m

= 0.01 kg/m

Mass per unit length of CD

= 8 gm/m

= 0.008 kg/m

For the string CD,

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

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

$=2\times 10\sqrt{10}$

$=20\times 3.14=63ms$

For the string AB,

$T=2\times 3.2g=6.4\times g$

$=64N$

$\Rightarrow v=\sqrt{\frac{T}{m}}$

$=\sqrt{\left(\frac{64}{0.01}\right)}=\sqrt{6400}$

$=80m/s$