1. Tardigrade
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  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

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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

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Solution:

$t _{1}= 2 5 6 H z$
For turning fork, where $f _{2}- f _{1}=\pm 5$
$f _{2}=$ frequency of piano
$f _{2}=( 2 5 6 + 5 ) H z$ or $( 2 5 6 - 5 ) H z$
When tension is increased the beat frequency decreases to 2 beats per second. If we assume that frequency of piano string is $261 Hz$. Then on increasing tension frequency, more than $261 Hz$. But it is given that beat frequency decreases, therefore $261 Hz$ is not post.
$\therefore ( 2 5 6 - 5 ) H z$