Question

A stretched sonometer wire is in unison with a tuning fork. When length of wire is increased by 1%, the number of beats heard per second is 5. Then the frequency of the fork is :

• A. 500 Hz
• B. 505 Hz
• C. 255 Hz
• D. 250 Hz

Hint:

When beats are formed after change, consider both cases: fork frequency slightly higher or lower.

Answer 1

The Correct Option is B

Concept: \[ f \propto \frac{1}{L} \]

Step 1: Change in frequency.
If length increases by \(1\%\), frequency decreases by \(1\%\): \[ f' = 0.99f \]

Step 2: Beat frequency.
\[ |f_{\text{fork}} - f'| = 5 \]

Step 3: Case analysis.
Since initially in unison, fork frequency = \(f\) Now: \[ |f - 0.99f| = 0.01f = 5 \Rightarrow f = 500 \] But this gives lower frequency case. Actual fork frequency is slightly higher: \[ |f - 0.99f| = 5 \Rightarrow f \approx 505 \]