Question

Two blocks each having mass 3.2kg are connected by wire CD and system is suspended from ceiling by another wire ab. The linear mass density of wire ab is 10gm/m and that of CD is 8 gm /m. Find the speed of transverse wave pulse produce in part ab and CD.

Answer 1

speed of transverse through stretched string is v = √{T/u}
where T is tension and u is mass density.

u for CD = 8gm/m = 8 × 10^-3 Kg/m
u for AB = 10gm/m = 10^-2 Kg/m

for CD rope, speed of transverse wave
tension for wire CD = mg = × 3.2 × 10 = 32N
$V_{CD}=\sqrt{\frac{T_{CD}}{\mu}} = \sqrt{ \frac{32}{8 \times {10}^{ - 3} } } = \sqrt{4000}$
hence, speed of wave in CD ≈63 m/s

similarly,
tension in CD = 2mg
= 2 × 3.2 × 10 = 64 N
$V_{AB}=\sqrt{\frac{T_{AB}}{\mu}} = \sqrt{ \frac{64}{ {10}^{ - 2} } } = \sqrt{6400}=80$

hence, speed of wave in AB = 80 m/s