Question

Figure shows a string of linear mass density $1.0\text{g/cm}$ on which a wave pulse is travelling.


Find the time taken by the pulse in travelling through a distance of $50\text{cm}$ on the string. Take $g=10{\text{m/s}}^2$

• A. $0.04\text{s}$
• B. $0.03\text{s}$
• C. $0.05\text{s}$
• D. $0.08\text{s}$

Answer 1

The correct option is C $0.05\text{s}$

Applying equilbrium condition for $1\text{kg}$ block along vertical direction,
$T=mg=10\text{N}$
The tension in the string is $10\text{N}$.
The mass per unit length of string is,
$\mu =1\text{g/cm}=0.1\text{kg/m}$.
Therefore the wave velocity is,
$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{10}{0.1}}=10\text{m/s}$
The time taken by the pulse in travelling through distance $d=50\text{cm}=0.5\text{m}$,
$\Rightarrow t=\frac{d}{v}=\frac{0.5}{10}=0.05\text{s}$.