The frequency of sonometer wire is f , but when the weights producing the tensions are completely immersed in water, the frequency becomes f / 2 and on immersing the weights in a certain liquid, the frequency becomes f / 3 . The specific gravity of the liquid is

Step-by-step solution

f T aligned f _ air f _ water & = W_ air W_ water = V g V g-V _w g & = f f 2 = - _w aligned aligned & & 2 & = - _w & & 4 -4 _w & = & & & = 4 3 _w aligned Similarly in second case, f f 3 = - _L 3= 4 3 _w 4- 3 _L _w = 4 4- 3 _L _w Here, _L _w = specific gravity (say S ) array cc & 9= 4 4-3 S & 36-27 S=4 S= 32 27 array