(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

$A$ set of $20$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \; Hz$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first,then the frequency of the last fork is $\dots \; Hz$.

DifficultJEE MAIN 2022

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The string of a violin emits a note of $205 \,Hz$ at its correct tension. The string is tightened slightly and then it produces six beats in two seconds with a tuning fork of frequency $205 \,Hz$. The frequency of the note emitted by the taut string is .......... $Hz$.

Easy

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The wavelengths of two sound notes in air are $\frac{40}{195} \,m$ and $\frac{40}{193} \,m$. Each note produces $9$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is

DifficultAP EAMCET 2011

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In Melde's experiment in the transverse mode,the frequency of the tuning fork and the frequency of the waves in the strings are in the ratio

Easy

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Two identical piano wires have a fundamental frequency of $600 \text{ Hz}$ when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of $6$ beats per second when both wires vibrate simultaneously?

DifficultTS EAMCET 2009

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$A$ set of $20$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \; Hz$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first,then the frequency of the last fork is $\dots \; Hz$.

The string of a violin emits a note of $205 \,Hz$ at its correct tension. The string is tightened slightly and then it produces six beats in two seconds with a tuning fork of frequency $205 \,Hz$. The frequency of the note emitted by the taut string is .......... $Hz$.

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