A sonometer wire resonates with a given tuning fork forming a standing wave 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' kg, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. Find the value of `M`.

Options

A. 25 g
B. 5 kg
C. 12.5 kg
D. `(1)/(25) kg`

Answer

A

Explanation

Let `f_(0)` = frequency of tuning fork
(`mu` = mass per unit length of wire) `= (3)/(2l) sqrt((Mg)/(mu))`
Solving this, we get M = 25 kg
In the first case frequency corresponds to fifth harmonic while in the second case it corresponds to third harmonic.