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(B) The frequency of string $A$ is $f_A = 320 \ Hz$. Let the frequency of string $B$ be $f_B$. The beat frequency is given by $n = |f_A - f_B| = 8 \ H

Vedclass · Accepted Answer

$312$

Vedclass · Answer

(B) The frequency of string $A$ is $f_A = 320 \ Hz$. Let the frequency of string $B$ be $f_B$. The beat frequency is given by $n = |f_A - f_B| = 8 \ Hz$. This implies $f_B = 320 \pm 8$,so $f_B$ could be $312 \ Hz$ or $328 \ Hz$. When the tension in string $A$ is reduced,its frequency $f_A$ decreases because $f \propto \sqrt{T}$. Let the new frequency be $f_A'$. Since $f_A' If $f_B = 312 \ Hz$,then $f_A' - 312 = 4 \implies f_A' = 316 \ Hz$ (which is less than $320 \ Hz$,consistent). If $f_B = 328 \ Hz$,then $328 - f_A' = 4 \implies f_A' = 324 \ Hz$ (which is greater than $320 \ Hz$,inconsistent). Therefore,the frequency of $B$ must be $312 \ Hz$.

Two vibrating strings $A$ and $B$ produce beats of frequency $8 \ Hz$. The beat frequency is found to reduce to $4 \ Hz$ if the tension in the string $A$ is slightly reduced. If the original frequency of $A$ is $320 \ Hz$,then the frequency of $B$ is: (in $Hz$)

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