A tuning fork of frequency n produces x beats | vedclass

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Question

(B) The beat frequency is given by $|n - f_s| = x$, where $f_s$ is the frequency of the sonometer string. This implies $f_s = n + x$ or $f_s = n - x$.

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$n - x$

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(B) The beat frequency is given by $|n - f_s| = x$, where $f_s$ is the frequency of the sonometer string. This implies $f_s = n + x$ or $f_s = n - x$. When the tension $T$ of the string is increased, the frequency of the string $f_s$ increases because $f_s \propto \sqrt{T}$. If $f_s = n + x$, increasing $f_s$ will make it move further away from $n$, thus increasing the beat frequency $(f_s - n)$. If $f_s = n - x$, increasing $f_s$ will make it move closer to $n$, thus decreasing the beat frequency $(n - f_s)$. Since the problem states that the beat frequency decreases, the initial frequency of the string must have been $n - x$.

$A$ tuning fork of frequency $n$ produces $x$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces lesser beats per second than before?

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