Question

A stretched sonometer wire resonates at a frequency of $350\text{Hz}$ and at the next higher frequency of $420\text{Hz}$. The fundamental frequency of this wire is :

• A. $350\text{Hz}$
• B. $5\text{Hz}$
• C. $70\text{Hz}$
• D. $170\text{Hz}$

Answer 1

The correct option is C $70\text{Hz}$

Given sonometer vibrates at;
$f_1=\frac{nv}{2L}=350\text{Hz}$
$f_2=\frac{(n+1)v}{2L}=420\text{Hz}$
Now, $f_2-f_1$, we get
$\frac{(n+1)v}{2L}-\frac{nv}{2L}=420-350$
$\frac{v}{2L}=70\text{Hz}$
This is the fundamental frequency