Question
A stone hangs in the air from a wire stretched over a sonometer. The wire is in unison with a tuning fork for distance l1 between the bridges. When the stone is dipped in water, the length between the bridges must be altered to l2 to bring it again in unison. Find the relative density of stone.
Solution
Let a be the density, V be the volume of stone and v be the frequency of tuning fork.
When the stone is in air, the tension in the string is Vag.
The wire is in unison for distance /, between the bridges, therefore
...(1)
When the stone is put in water, due to upward thrust on the stone, the tension in the string decreases to F(σ-1)g.
Now the wire is in unison for distance l2 between the bridges.
Thus,
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...(2)
From (1) and (2),
, is the relative density of the stone.
When the stone is in air, the tension in the string is Vag.
The wire is in unison for distance /, between the bridges, therefore
...(1) When the stone is put in water, due to upward thrust on the stone, the tension in the string decreases to F(σ-1)g.
Now the wire is in unison for distance l2 between the bridges.
Thus,
...(2) From (1) and (2),
, is the relative density of the stone. 
