A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

Solution

Physics sir · 3 steps

Filing a fork raises its pitch, so A must start below 340 Hz for the beats to fall.

1. Two candidates. Beat frequency is the difference of the two frequencies, so |f_A - 340| = 5. That gives f_A = 335 Hz or f_A = 345 Hz.
2. Effect of filing. Filing removes metal from the prongs, so they get lighter and vibrate faster. Filing always increases the frequency of a fork.

   Starting f_A	After filing	Beats with 340 Hz	Matches?
   335 Hz	rises towards 340, reaches 338 Hz	5 → 2, decreases	yes
   345 Hz	rises away from 340	5 → more than 5, increases	no

3. So. Only a fork starting below 340 Hz can have its beats drop when filed. The frequency of fork A is 335 Hz, option (a).

The idea to keep. Beats give two possible frequencies. Then ask which way the change moves the fork: filing raises frequency, loading with wax lowers it. Keep the root whose beats change the way the question says.

Answer from the NTA final answer key. Solution by PrepWiser.