A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Question

A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was (A) 510 Hz (B) 514 Hz (C) 516 Hz (D) 508 Hz

Tardigrade Admin · Accepted Answer

Let the frequencies of tuning fork and piano string be

v_{1}

and

v_{2}

respectively

∴ v_{2} = v_{1} \pm 4 = 512 Hz \pm 4

= 516 Hz

or

508 Hz

Increase in the tension of a piano string increases its frequency
If

v_{2} = 516 Hz

, further increase in

v_{2}

, resulted in an increase in the beat frequency. But this is not given in the question.
If

v_{2} = 508 Hz

, further increase in

v_{2}

resulted in decrease in the beat frequency. This is given in the question. When the beat frequency decreases to

2

beats per second. Therefore, the frequency of the piano string before increasing the tension was

508 Hz

.

Q. A tuning fork of frequency 512Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

510 Hz

514 Hz

516 Hz

508 Hz

Q. A tuning fork of frequency $512 Hz$ makes $4$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was