Question

A wire is in unison with a fork of frequency 250 Hz, when stretched by a weight hanging vertically. On immersing the weight in water, the wire produces ten beats per second with the same fork. Calculate density of material of weight, if density of water is $1g/c{m}^3$.

Answer 1

We get

$f\alpha \sqrt{T}$ Where $d$+density of substance

$s=$density of water

$\begin{array}{c}\Rightarrow \frac{f_1}{f_2}=\sqrt{\frac{T_1}{T_2}}\\ \Rightarrow \frac{250}{240}=\sqrt{\frac{dvg}{\left(s-d\right)vg}}\\ \Rightarrow \frac{625}{576}=\frac{d}{s-d}\\ \Rightarrow 625s-625d=576d\\ \Rightarrow 625s=\left(576+525\right)d\\ \Rightarrow 625s=\left(1211\right)d\\ f=\frac{625}{1211}\times 1=0.51gm/cc\end{array}$