Figure (15-E11) shows a string stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a particular tuning fork. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the density of the material of the block.

Question

Philoid · Accepted Answer

58 × 10³ kg m⁻³

Suppose, the density of the material of block is

So, tension force of rope here balances the gravitational force.

So,

Now,

Or,

Now, the block is immersed in water, so buoyance force must be present there.

B=

Or, T = Weight - Buoyance= (ρ-ρ_w)V_g

The tuning fork is same,

f₁₀=f₁₁

Computing these two, we get,