(C) Let the frequency of the unknown tuning fork be $f$.The number of beats produced by $A$ $(256 \ Hz)$ and the unknown fork is $|f - 256|$.The numbe

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(C) Let the frequency of the unknown tuning fork be $f$.The number of beats produced by $A$ $(256 \ Hz)$ and the unknown fork is $|f - 256|$.The number of beats produced by $B$ $(262 \ Hz)$ and the unknown fork is $|f - 262|$.According to the problem,the number of beats with $B$ is double the number of beats with $A$:$|f - 262| = 2 |f - 256|$.Case $1$: $f - 262 = 2(f - 256)$$f - 262 = 2f - 512$$f = 512 - 262 = 250 \ Hz$.Case $2$: $f - 262 = -2(f - 256)$$f - 262 = -2f + 512$$3f = 774$$f = 258 \ Hz$.Checking the options,$250 \ Hz$ is provided as option $C$.

Class 11 Physics Waves and Sound Beats and Tuning fork

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Two tuning forks have frequencies $256 \ Hz$ $(A)$ and $262 \ Hz$ $(B)$. Tuning fork $A$ produces a certain number of beats per second with an unknown tuning fork. The same unknown tuning fork produces double the number of beats per second with tuning fork $B$. What is the frequency of the unknown tuning fork in $Hz$?

A
$262$
B
$260$
C
$250$
D
$300$

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Class 11

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Waves and Sound

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Beats and Tuning fork

Two sitar strings,$A$ and $B$,playing the note $'Dha'$ are slightly out of tune and produce beats at a frequency of $5 \, Hz$. The tension of string $B$ is slightly increased and the beat frequency is found to decrease to $3 \, Hz$. If the frequency of $A$ is $425 \, Hz$,the original frequency of $B$ is ... $Hz$.

DifficultJEE MAIN 2018

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$50$ tuning forks are arranged in increasing order of their frequencies such that each gives $4 \, \text{beats/sec}$ with its previous tuning fork. If the frequency of the last fork is the octave of the first, then the frequency of the first tuning fork is ... $Hz$.

Easy

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Two tuning forks $X$ and $Y$ have frequencies $280 \,Hz$ and $284 \,Hz$. $A$ third tuning fork $Z$ has an unknown frequency. When $X$ and $Z$ are sounded together, a certain number of beats per second are heard. When $Y$ and $Z$ are sounded together, the beat frequency is found to be three times as great. The frequency of $Z$ is: (in $\,Hz$)

DifficultAP EAMCET 2020

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Two waves $Y_1 = 0.25 \sin(316t)$ and $Y_2 = 0.25 \sin(310t)$ are propagating along the same direction. The number of beats produced per second is:

DifficultMHT CET 2020

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Two sitar strings $A$ and $B$ playing the note 'Dhai' are slightly out of tune and produce beats of frequency $5 \; Hz$. The tension of the string $B$ is slightly increased and the beat frequency is found to decrease to $3 \; Hz$. What is the original frequency of $B$ if the frequency of $A$ is $427 \; Hz$ (in $; Hz$)?

Easy

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$50$ tuning forks are arranged in increasing order of their frequencies such that each gives $4 \, \text{beats/sec}$ with its previous tuning fork. If the frequency of the last fork is the octave of the first, then the frequency of the first tuning fork is ... $Hz$.

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