Question

A tuning fork of frequency $f$ produces $4beats$ for both $95cm$ and $100cm$ long sonometer wire. Value of $f$ is

• A. $152Hz$
• B. $156Hz$
• C. $160Hz$
• D. $164Hz$

Answer 1

Answer: (B)

According the the data given in the problem
$l_1=95cm{l}_2=100cm$
We know that
$n\propto \frac{1}{l}\therefore \frac{n_1}{n_2}=\frac{l_2}{l_1}$
It is given that beat frequency is $4Hz$ , so we can write
$\frac{n+4}{n-4}=\frac{100}{95}=\frac{20}{19}$
$\Rightarrow 19n+76=20n-80$
Solving it further
$n=156Hz$