Question

A steel wire of mass $8\text{g}$ and length $160\text{cm}$ is fixed at two ends. The tension in the wire is $50\text{N}$. Find the frequency and wavelength of the fourth harmonic.

• A. $125\text{Hz},40\text{cm}$
• B. $250\text{Hz},40\text{cm}$
• C. $125\text{Hz},80\text{cm}$
• D. $250\text{Hz},80\text{cm}$

Answer 1

The correct option is C $125\text{Hz},80\text{cm}$

Given that
$m=8\text{g}\text{or}8\times {10}^{-3}\text{kg}$
$l=160\text{cm}\text{or}1.6\text{m}$
$T=50\text{N}$
So ,
Linear mass density $\left(\mu \right)=\frac{m}{l}=\frac{8\times {10}^{-3}}{1.6}=0.5\times {10}^{-2}\text{kg/m}$

Now,

Wave speed $\left(v\right)=\sqrt{\frac{50}{0.5\times {10}^{-2}}}=100\text{m/s}$

For fourth harmonic,
$f_4=\frac{4v}{2l}=\frac{4\times 100}{2\times 1.6}=125\text{Hz}$
and
For wavelength,
$\lambda =\frac{v}{f}=\frac{100}{125}=0.8\text{m}\text{or}80\text{cm}$

Thus, option (c) is the correct answer.