Q. A tuning fork vibrating with a sonometer having $20\ cm$ wire produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to $21\ cm.$ The frequency of the tuning fork (in Hertz) must be
A) 200
B) 210
C) 205
D) 215
Explanation
(c) Let the frequency of tuning fork be $N$
As the frequency of vibration string $\propto \frac{1}{length\ ofstring}$
For sonometer wire of length $20\ cm,$ frequency must be $(N + 5)$ and that for the sonometer wire of length $21cm,$ the frequency must be $(N - 5)$ as in each case the tunning fork produces 5 beats/sec with sonometer wire
Hence $n_{1}l_{1} = n_{2}l_{2} \Rightarrow (N + 5) \times 20 = (N - 5) \times 21$
$\Rightarrow N = 205\ Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.