Question

A tuning fork of frequency \(n\) produces \(x\) beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces lesser beats per second than before?

• A. \(n+x\)
• B. \(n-x\)
• C. \((n+x)^2\)
• D. \((n-x)^2\)

Hint:

Tension up means string frequency up. Beats fall only if the string was below the fork frequency.

Answer 1

The Correct Option is B

Step 1: Effect of tension
\(f\propto\sqrt T\), so a slight increase in tension raises the string frequency.

Step 2: Two cases
If \(f_s=n+x\), a rise moves it farther from \(n\) and the beats increase.
If \(f_s=n-x\), a rise moves it closer to \(n\) and the beats decrease.

Step 3: Choose
The beats decreased, so \(f_s=n-x\). Option (B).

Final Answer:
The string frequency was \(n-x\), option (B). \[ \boxed{\text{(B)}} \]