1. Tardigrade
  2. Question
  3. Physics
  4. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9kg$ is suspended from the wire. When this mass is replaced by a mass $M,$ the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$ is:

NTA AbhyasNTA Abhyas 2020

Solution:

Solution
$F=\frac{n}{2 l}\sqrt{T / \mu }$ { $n \rightarrow n^{t h}$ Harmonic or $n$ anti nodes}
In case $\left(\right.i\left.\right)$ $f=\frac{5}{2 l}\sqrt{\frac{90}{\mu }}$
In case $\left(\right.ii\left.\right)$ $f=\frac{3}{2 l}\sqrt{\frac{T}{\mu }}$
$\Rightarrow T=50N$ or $M=5kg$