Question

A tuning fork produces 4 beats/second from the stretched string of a sonometer of length 0.49 m and 0.50 m. Calculate the frequency of the tuning fork.

Answer 1

Frequency of the sonometer wire $\propto \frac{1}{l}$

Frequency of the tuning fork = n

Then frequency of 0.49 m length of wire = n + 4

and frequency of 0.50 m length of wire = n - 4

$\because n\propto \frac{1}{l}$

$\therefore \frac{n_1}{n_2}=\frac{l_2}{l_1}$

or $\frac{n+4}{n-4}=\frac{0.50}{0.49}=\frac{50}{49}$

or 50 (n - 4) = 49 (n + 4)

or 50 n - 200 = 49 n + 196

or 50 n - 49 n = 196 + 200

or n = 396 Hz