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  4. 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

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Q. 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

AMUAMU 2013Waves

Solution:

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
$= \frac{2.45 \times 2}{4.9} = 1.0 \,s$