Question

A uniform rope of mass $0.1 \,kg$ and length $2.45 \,m$ hangs from a ceiling. The time taken by a transverse wave to travel the full length of the rope is

• A. $1.2\,s$
• B. $1.0\,s$
• C. $2.2\,s$
• D. $3.1\,s$

Answer 1

Answer: (B)

$1.0\,s$

Answer 2

Velocity of transverse wave is given by
$v = \sqrt{\frac{T}{m}}$
$T :$ Tension in string
$m :$ Mass per unit length
$\Rightarrow v = \sqrt{\frac{0.1 \times 9.8}{(0.1 /2.45)}}$
$= \sqrt{9.8\times 2.45}$
$= 4.9 \,m/s$
Now, time taken by wave to travel full length of the rope
$= \frac{2.45 \times 2}{4.9} = 1.0 \,s$