A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ Hz. Numerical answer type. Work it out, then open the answer.

Answer: 6. f ∝ √(T); at 6 N the wire is in unison with the fork, so f = n. At 54 N: f' = n√(54/6) = 3n. 3n - n = 12 ⇒ n = 6 Hz So the frequency of the fork is 6 Hz.

A tuning fork resonates with a sonometer wire of length 1 m stretched… | JEE Main 2024 (1 Feb, Shift 1)

Q36JEE Main 2024 · 1 FEB · SHIFT 1Medium

Beats

A tuning fork resonates with a sonometer wire of length $1\text{ m}$ stretched with a tension of $6\text{ N}$ . When the tension in the wire is changed to $54\text{ N}$ , the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ $\text{Hz}$ .

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 6

$f \propto \sqrt{T}$ ; at 6 N the wire is in unison with the fork, so $f = n$ .
At 54 N: $f' = n\sqrt{54/6} = 3n$ .
$3n - n = 12 \Rightarrow n = 6\text{ Hz}$
So the frequency of the fork is $6\text{ Hz}$ .

Report a mistake

Beats question from JEE Main 2024 (1 Feb, Shift 1)

More questions on Beats