Question

A tuning fork of frequency 392 Hz resonates with 50 cm length of a string under tension T. If the mass of the string is decreased by 2%, keeping the tension constant, the number of beats heard when the string and the tuning fork are made to vibrate simultaneously is

• A. 4
• B. 6
• C. 8
• D. 12

Hint:

For small changes: (Δ f)/(f) ≈ -(1)/(2)(Δ μ)/(μ)

Answer 1

The Correct Option is A

Step 1: Frequency of string f ∝ \frac1√(μ)
Step 2: Decrease in mass density by 2% increases frequency by approximately 1%.
Step 3: New frequency of string f' ≈ 392 × 1.01 ≈ 396 Hz
Step 4: Number of beats |f' - f| ≈ 4