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) $0.05\text{s}$

Given figure is

Now,

Let tension in the string is F
Applying equilibrium condition for $1\text{kg}$ block along vertical direction,
$F=mg=10\text{N}$
The tension in the string is $10\text{N}$.

According to the question

The mass per unit length of string is,

$\mu =1\text{g/cm}=0.1\text{kg/m}$.

We know,
The wave velocity is given as,
$v=\sqrt{\frac{F}{\mu }}=\sqrt{\frac{10}{0.1}}=10\text{m/s}$

Hence the wave velocity is 10 m/s

Now,
The time taken by the pulse in travelling through distance $d=50\text{cm}=0.5\text{m}$,
$\Rightarrow t=\frac{d}{v}=\frac{0.5}{10}=0.05\text{s}$.

Hence the time taken is 0.05 s.