Resonance is produced between a turning fork and a resonance column tube with upper end open and lower end closed by water surface. If the frequency of the tuning fork is 800 Hz , and first two resonances are observed at lengths $9.75 \mathrm{~cm}, 31.25 \mathrm{~cm}$,

Find the length at which the third resonance occurs? Also find the speed of sound.

The speed of transverse wave in aluminium wire is $\frac{1}{10}$ times the speed of longitudinal wave in the wire. The stress in the wire is (Young's Modulus of Al=10 ${ }^{10} \mathrm{~Pa}$ )

The fundamental frequency of sound produced in an open pipe of length $\mathbf{L}_1$ is same as the frequency of the $3^{\text {rd }}$ harmonic of the sound produced in the closed pipe of length $\mathbf{L}_2$ Then the ratio of $\frac{L_1}{L_2}$ is :

An open pipe is in second harmonic with frequency $f_1$. One end of the tube is closed and frequency is increased to $f_2$ and it resonates again with nth harmonic. For what value of n , the ratio of $\frac{f_1}{f_2}$ is $\frac{4}{5}$ ?