A sonometer wire resonates with a given tunin | vedclass

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

Question

(A) The frequency of a sonometer wire is given by the formula $n = \frac{p}{2L} \sqrt{\frac{T}{\mu}}$,where $p$ is the number of loops (antinodes),$L$

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(A) The frequency of a sonometer wire is given by the formula $n = \frac{p}{2L} \sqrt{\frac{T}{\mu}}$,where $p$ is the number of loops (antinodes),$L$ is the length,$T$ is the tension $(T = Mg)$,and $\mu$ is the linear mass density.Since the frequency $n$,length $L$,and linear mass density $\mu$ remain constant,we have $p \propto \sqrt{T} \propto \sqrt{M}$.For the first case: $p_1 = 5$ and $M_1 = 9 \ kg$.For the second case: $p_2 = 3$ and $M_2 = m$.Using the ratio: $\frac{p_1}{p_2} = \sqrt{\frac{M_1}{M_2}}$.Substituting the values: $\frac{5}{3} = \sqrt{\frac{9}{m}}$.Squaring both sides: $\frac{25}{9} = \frac{9}{m}$.Solving for $m$: $m = \frac{9 	imes 9}{25} = \frac{81}{25} = 3.24 \ kg$. Wait,re-evaluating the relationship: $p_1 \sqrt{M_1} = p_2 \sqrt{M_2}$.$5 \sqrt{9} = 3 \sqrt{m} \implies 5 	imes 3 = 3 \sqrt{m} \implies 5 = \sqrt{m} \implies m = 25 \ kg$.

Similar Questions

Two tuning forks when sounded together produce $4$ beats per second. One of the forks is in unison with $23 \ cm$ length of a sonometer wire and the other with $24 \ cm$ length of the same wire. The frequencies of the two tuning forks are

The length of the wire shown in the figure between the pulleys is $1.5 \, m$ and its mass is $12.0 \, g$. The frequency of vibration with which the wire vibrates in three loops,forming an antinode at the midpoint of the wire,is: (Given $g = 9.8 \, m/s^2$)

$A$ string $2.0\, m$ long and fixed at its ends is driven by a $240\, Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency are:

$A$ string is stretched between two rigid supports separated by $75 \,cm$. There are no resonant frequencies between $420 \,Hz$ and $315 \,Hz$. The lowest resonant frequency for the string is (in $\,Hz$)

If the tension of a sonometer wire increases four times,then the fundamental frequency of the wire will increase by how many times?

Vedclass Test Series

Exam Paper Generator

Online Exam Module