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

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

Tardigrade Admin · Accepted Answer

Velocity of transverse wave is given by

v = \frac{T}{m}

T :

Tension in string

m :

Mass per unit length

\Rightarrow v = \frac{0.1 \times 9.8}{( 0.1/2.45 )}

= 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

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

1.2 s

1.0 s

2.2 s

3.1 s

Velocity of transverse wave is given by v=mT​​ T: Tension in string m: Mass per unit length ⇒v=(0.1/2.45)0.1×9.8​​ =9.8×2.45​ =4.9m/s Now, time taken by wave to travel full length of the rope =4.92.45×2​=1.0s

Q. A uniform rope of mass $0.1 k g$ 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

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