Question

A tuning fork of freqqency 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

Answer 1

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 508 Hz.

• Option (d) is correct.
• The frequency of piano string = 512 ± 4
• = 516 or 508
• The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased.  
• It means that the frequency of the piano string before increasing the tension was
• 508 Hz.

Answer 2

The frequency of the piano string before increasing the tension is 508 Hz.

Option (D) is correct.

Explanation:

The frequency of tuning fork, nf = 512 Hz

Beat frequency, x = 4 betas / sec

Beat frequency decrease to 2 beats per second.

We have to find the frequency of the piano np.

We have the equation:

np = nf - x = 512 - 4 = 508 Hz

When tension is increased then frequency is also increased.

as number of beats decrease the frequency of string must be less than 512 Hz.

Thus the frequency of the piano string before increasing the tension is 508 Hz.

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