1. Tardigrade
  2. Question
  3. Physics
  4. A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A tuning fork of known frequency $256 Hz$ makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Waves

Solution:

The possible frequencies of piano are
$(256+5) Hz$ and $(256-5) Hz$
image
For piano string, $v=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$
When tension $T$ increases, $v$ increases
(i) If $261 Hz$ increases, beats/sec increase. This is not given in the question.
(ii) If $251 Hz$ increases due to tension, beats per second decrease. This is given in the question.
Hence frequency of piano $=(256-5) Hz$