Question

In an experimental setup shown below


A block of mass $m=10\text{kg}$ is hanging. If mass of string is $0.01\text{kg}$ and length of string is $1\text{m}$. Find the number of loop formed if a standing wave is set on the string. Frequency of the wave is given as $50\text{Hz}$.

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

The correct option is A $1$

Mass per unit length of the string

$\mu =\frac{0.01}{1}=0.01{\text{kg m}}^{-1}$

Tension on the string

$T=mg=10\times 10=100\text{N}$

The velocity of the wave on a string is given by

$V=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{100}{0.01}}=\sqrt{10000}$

$\Rightarrow V=100{\text{ms}}^{-1}$

The relation between wave velocity, frequency and wavelength is given by,

$\lambda =\frac{V}{f}$

$\Rightarrow \lambda =\frac{100}{50}=2\text{m}$

The length of one loop $=\frac{\lambda }{2}$

$\Rightarrow$ The length of one loop $=1\text{m}$

Given that the length of the string is $1\text{m}$,

$\therefore$ The number of loops formed in the string will be $1$.

Hence, option $\left(A\right)$ is correct.