Question 504: Waves

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

Accepted Answer

Let the frequencies of tuning fork and piano string be $${\upsilon _1}$$ and $${\upsilon _2}$$ respectively.
$$ 	herefore $$ $${\upsilon _2} = {\upsilon _1} \pm 4 = 512\,Hz \pm 4$$
= 516 Hz  or  508 Hz
Increase in the tension of a piano string increases its frequency.
If $${\upsilon _2}$$ = 516 Hz, further increase in $${\upsilon _2}$$, resulted in an increase in the beat frequency. But this is not given in the question.
If $${\upsilon _2}$$ = 508 Hz, further increase in $${\upsilon _2}$$ 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.

Answer

510 Hz

Answer

514 Hz

Answer

516 Hz

Answer

508 Hz

Waves

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

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