Question

A tuning fork of frequency $200\text{Hz}$ is vibrating with a sonometer wire to produce $10\text{beats/sec}$. When the tension in the sonometer wire is increased, beat frequency decreases. Original frequency of the sonometer wire in $\text{Hz}$ is

Answer 1

Given that, initially,
$|f_1-f_2|=10\text{Hz}$
& $f_2=200\text{Hz}$

where $f_1=$ original frequency of sonometer wire
$f_2=$ frequency of tuning fork

When tension in sonometer wire is increased, new frequency $f_1^{\prime }>f_1$
[since $f\propto \sqrt{\frac{T}{\mu }}$]

Since beat frequency decreases, we can say that, $f_2>f_1$ initially
$\therefore f_1=200-10=190\text{Hz}$