• question_answer A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg 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:- A)  $25\text{ }kg$             B)  $5\text{ }kg$C)  $12.5\text{ }kg$           D)  $\frac{1}{25}\,\,kg$

Solution :

$n=\frac{P}{2\ell }\,\sqrt{\frac{T}{m}}$ No. of loops = No. of antinodes ${{n}_{1}}=\frac{5}{2\ell }\sqrt{\frac{9g}{m}},$     ${{n}_{2}}=\frac{3}{2\ell }\sqrt{\frac{Mg}{m}}$ $\because$ ${{n}_{1}}={{n}_{2}}\Rightarrow \,\frac{5}{2\ell }\sqrt{\frac{9g}{m}}=\frac{3}{2\ell }\sqrt{\frac{Mg}{m}}\Rightarrow M=25\,kg$

You need to login to perform this action.
You will be redirected in 3 sec