In an experiment with sonometer a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. Tension of the string remaining constant the frequency of the second tuning fork is :

Question

In an experiment with sonometer a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. Tension of the string remaining constant the frequency of the second tuning fork is : (A) 163.84 Hz (B) 400 Hz (C) 320 Hz (D) 204.8 Hz

Tardigrade Admin · Accepted Answer

For sonometer n propto (1/l) ∴ (n1/n2) = (l2/l1) ⇒ (256/n2) = (16/25) n2 = (256 × 25/16) = 400 Hz

Q. In an experiment with sonometer a tuning fork of frequency $256 Hz$ resonates with a length of $25 c m$ and another tuning fork resonates with a length of $16 c m$ . Tension of the string remaining constant the frequency of the second tuning fork is :

163.84 Hz

400 Hz

320 Hz

204.8 Hz

For sonometer $n \propto \frac{1}{l}$
$∴ \frac{n _{1}}{n _{2}} = \frac{l _{2}}{l _{1}} \Rightarrow \frac{256}{n ^{2}} = \frac{16}{25}$
$n_{2} = \frac{256 \times 25}{16}$
$= 400 Hz$

Q. In an experiment with sonometer a tuning fork of frequency 256Hz resonates with a length of 25cm and another tuning fork resonates with a length of 16cm. Tension of the string remaining constant the frequency of the second tuning fork is :