A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity

Question

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to\

Professor PC Thomas Classes · Answer

(c) : Due to jagged end $$\begin{equation*} \frac{v}{4(11-x) 	imes 10^{-2}}=512 	ag{i} \end{equation*}$$$$\begin{equation*} \frac{v}{4(27-x) 	imes 10^{-12}}=256 	ag{ii} \end{equation*}$$ From eqn. (i) and (ii), $2(11-x)=(27-x)$\ $\Rightarrow x=-5 \mathrm{~cm}$\ From eqn. (i), $\frac{v}{4 	imes 16 	imes 10^{-2}}=512$\ $\Rightarrow \quad v \simeq 328 \mathrm{~m} \mathrm{~s}^{-1}$\