50 tuning forks are arranged in increasing or | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the frequency of the first tuning fork be $n_1 = n \, 	ext{Hz}$.Since there are $N = 50$ tuning forks and each gives $4 \, 	ext{beats/sec}$

Vedclass · Accepted Answer

$196$

Vedclass · Answer

(C) Let the frequency of the first tuning fork be $n_1 = n \, 	ext{Hz}$.Since there are $N = 50$ tuning forks and each gives $4 \, 	ext{beats/sec}$ with the previous one, the frequencies form an arithmetic progression with common difference $d = 4 \, 	ext{Hz}$.The frequency of the $N$-th tuning fork is given by $n_N = n_1 + (N - 1)d$.Substituting the values, $n_{50} = n + (50 - 1) 	imes 4 = n + 49 	imes 4 = n + 196$.Given that the frequency of the last fork is the octave of the first, we have $n_{50} = 2n$.Equating the two expressions: $2n = n + 196$.Solving for $n$: $n = 196 \, 	ext{Hz}$.

$50$ 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 ... $Hz$.

Similar Questions

The air columns in two tubes closed at one end vibrating in their fundamental modes produce $2$ beats per second. The number of beats produced per second when the same tubes are vibrated in their fundamental mode with their both ends open are

$A$ light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 \, cm$,the frequency of the tuning fork is .... $Hz$

The frequencies of two tuning forks $A$ and $B$ are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork $C$. When $A$ and $B$ are sounded together, $10$ beats are produced in $1 \text{ s}$. The frequency of tuning fork $C$ is: (in $\text{ Hz}$)

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?

Two tuning forks have frequencies $450\, Hz$ and $454\, Hz$ respectively. On sounding these forks together,the time interval between successive maximum intensities will be .... $sec$

Vedclass Test Series

Exam Paper Generator

Online Exam Module