(B) Let the frequency of the $1^{\text{st}}$ tuning fork be $n_1$.The frequencies are in an arithmetic progression with common difference $d = 5 \text

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(B) Let the frequency of the $1^{\text{st}}$ tuning fork be $n_1$.The frequencies are in an arithmetic progression with common difference $d = 5 \text{ Hz}$.The frequency of the $41^{\text{st}}$ tuning fork is given by $n_{41} = n_1 + (41 - 1) \times d$.$n_{41} = n_1 + 40 \times 5 = n_1 + 200$.Given that the frequency of the last fork is double the first,$n_{41} = 2n_1$.Substituting this into the equation: $2n_1 = n_1 + 200$.Solving for $n_1$: $n_1 = 200 \text{ Hz}$.Therefore,$n_{41} = 2 \times 200 = 400 \text{ Hz}$.

Class 11 Physics Waves and Sound Beats and Tuning fork

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$41$ tuning forks are arranged in increasing order of frequency such that each produces $5 \text{ beats/second}$ with the next tuning fork. If the frequency of the last tuning fork is double that of the frequency of the first fork,then the frequency of the first and last fork is:

MHT CET 2023 All MHT CET

A
$400, 200 \text{ Hz}$
B
$200, 400 \text{ Hz}$
C
$100, 200 \text{ Hz}$
D
$205, 410 \text{ Hz}$

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Waves and Sound

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Beats and Tuning fork

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$A$ tuning fork of frequency $512\, Hz$ makes $4$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was .... $Hz$

MediumAIPMT 2010

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$A$ tuning fork and an air column whose temperature is $51^{\circ} C$ produce $4$ beats in one second,when sounded together. When the temperature of the air column decreases,the number of beats per second decreases. When the temperature is $16^{\circ} C$,only one beat per second is produced. The frequency of the tuning fork is ........... $Hz$.

Medium

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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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Two tuning forks,$A$ and $B$,produce $4$ beats per second when sounded together. The frequency of $A$ is $320 \ Hz$. When some wax is added to $B$ and it is sounded with $A$,$4$ beats per second are again heard. The frequency of $B$ is .... $Hz$.

Medium

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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?

DifficultAP EAMCET 2009

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$41$ tuning forks are arranged in increasing order of frequency such that each produces $5 \text{ beats/second}$ with the next tuning fork. If the frequency of the last tuning fork is double that of the frequency of the first fork,then the frequency of the first and last fork is:

Similar Questions

$A$ tuning fork of frequency $512\, Hz$ makes $4$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was .... $Hz$

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 .......... $Hz$.

Two tuning forks,$A$ and $B$,produce $4$ beats per second when sounded together. The frequency of $A$ is $320 \ Hz$. When some wax is added to $B$ and it is sounded with $A$,$4$ beats per second are again heard. The frequency of $B$ is .... $Hz$.

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?

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