Question

A tuning fork vibrating with sonometre wire of length 20cm produces 5 beats per second . The beat frequency doesn't change if length of wire is changed to 21cm , the frequency of tuning fork is

• A. 280
• B. 190
• C. 205
• D. 210

Answer 1

The correct option is C 205

Fundamental frequency is

$n=\frac{\frac{1}{2}}{JT/m}n=\frac{1}{l}$

Assuming for $20cm$ frequency for $n_1$

for $21cm$ frequency is $n_2$

So $n_1/n_2=21/20$

Then $n_1=21x$ and $n_2=20x$

Let the frequency $nf$ for producing $5$ beats

So, $n_2>n_f>n_2$

So $n_1-n_f=521x-nf=5\to \left(1\right)$

and $nf-n_2=5n-20x=5\to \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we get $x=205Hz$