Wavelength of two notes in air are $\frac{66}{153} \mathrm{m}$ and$\frac{66}{151} \mathrm{m}$ . Each note produces $5$ beats per second with third note of a fixed frequency. Calculate the velocity of sound in air.

AB is a cylinder of length$1 \mathrm{metre}$ ,fitted with a thin flexible diaphragm C at the middle and two other thin flexible diaphragms A and B at the ends. The portions AC and BC contain hydrogen and oxygen gas respectively. The diaphragms A and B are set into vibrations of the same frequency. What is the minimum frequency of these vibrations for which diaphragm C is a node? Assume the velocity of sound in hydrogen to be $1100 \mathrm{m} {\mathrm{s}}^{-1}$ and in oxygen $300 \mathrm{m} {\mathrm{s}}^{-1}$ .

In the arrangement shown in figure the string has a mass of $20 \mathrm{g}$. The string goes round the pulley P and carries a mass $4 \mathrm{kg}$. The other end of the string is fixed to the ground. How much time (in seconds) will it take for a transverse vibration produced at the ground to reach the pulley P? Take, $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$.