A tuning fork of frequency 100 , Hz when soun | vedclass

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Question

(A) Let the known frequency be $n_A = 100 \, Hz$ and the unknown frequency be $n_B$.The beat frequency is given by $|n_A - n_B| = 2 \, Hz$. This impli

Vedclass · Accepted Answer

$102$

Vedclass · Answer

(A) Let the known frequency be $n_A = 100 \, Hz$ and the unknown frequency be $n_B$.The beat frequency is given by $|n_A - n_B| = 2 \, Hz$. This implies $n_B = 100 \pm 2$,so $n_B$ is either $102 \, Hz$ or $98 \, Hz$.When the unknown tuning fork is loaded,its frequency $n_B$ decreases $(n_B \downarrow)$.Case $1$: If $n_B = 98 \, Hz$,loading it further decreases the frequency (e.g.,to $97 \, Hz$). The new beat frequency would be $|100 - 97| = 3 \, Hz$,which is an increase.Case $2$: If $n_B = 102 \, Hz$,loading it decreases the frequency (e.g.,to $101 \, Hz$). The new beat frequency would be $|100 - 101| = 1 \, Hz$,which is a decrease.Since the problem states that the beat frequency decreases to $1 \, Hz$ after loading,the unknown frequency must be $102 \, Hz$.

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