Question

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 for. 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.
Figure

Answer 1

Density is $5.8 \times 10^3\ kgm^-^3$

Explanation:

• Let $\rho$ be density of block.

• Weight $\rho$ Vg where V = volume of Block

• The same turning fork resonates with the string in the two cases.

= $f_1_0 = \frac {10}{2l}\sqrt\frac{T - \rho_wVg}{m}$

= $\frac {11}{2l}\sqrt\frac{(\rho - \rho_w)Vg}{m}$

$\frac {10}{11} = \sqrt\frac{(\rho - \rho_w)}{m}$

$\frac{(\rho - 1)}{\rho} = \frac{100}{121}$ (because, $\rho_w = 1 gmcc&^-^1$)

$100\rho = 121\rho - 121$

$5.8 \times 10^3 kgm^-^3$