Question

A tuning fork and a vibrating sonometer wire gives 6 beats per second either with length of the wire 1.0 m or 1.06 m. The frequency of the fork is

• A. 200 Hz
• B. 206 Hz
• C. 212 Hz
• D. 218 Hz

Hint:

The longer wire gives the lower frequency; use \(f\propto1/L\) with the beat frequency.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Sonometer frequency is \(f\propto\dfrac{1}{L}\), so the 1.0 m wire gives a higher frequency than the 1.06 m wire.

Step 2: Set up
Let the fork have frequency \(n\). Then \(f_{1.0}=n+6\) and \(f_{1.06}=n-6\).

Step 3: Use inverse proportion
\(\dfrac{n+6}{n-6}=\dfrac{1.06}{1.0}\), so \(n+6=1.06n-6.36\).

Step 4: Calculation
\(0.06n=12.36\), so \(n=206\ \text{Hz}\).

Final Answer:
The frequency of the fork is 206 Hz. \[ \boxed{\text{(B) }206\text{ Hz}} \]