Question

Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

• A. $\frac{n}{3}$
• B. $n\sqrt{3}$
• C. $\frac{n}{3\sqrt{3}}$
  
• D. $\frac{n}{\sqrt{3}}$
  

Answer 1

The correct option is C $\frac{n}{3\sqrt{3}}$


Let $T_1=T,T_2=3T,l_1=l,l_2=3l,d_1=d,d_2=3d$

Fundamental frequency in a stretched string is given by

$n=\frac{1}{2l}\sqrt{\frac{T}{m}}$

$n=\frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}p}}$

$\Rightarrow n\alpha \frac{\sqrt{T}}{lr}$

$\Rightarrow \frac{n_1}{n_2}=\sqrt{\frac{T_1}{T_2}}\times \frac{l_2}{l_1}\times \frac{r_2}{r_1}$

$=\sqrt{\frac{T}{3T}}\times \frac{3l}{l}\times \frac{2r}{r}=3\sqrt{3}\Rightarrow n_2=\frac{n}{3\sqrt{3}}$

Final answer: (d)