A set of $10$ tuning forks is arranged in series of increasing frequency. If each fork gives $3$ beats with the preceding one and the last fork has twice the frequency of the first, then frequency of the first tuning fork is

A whistle $\text{'}S\text{'}$ of frequency $\nu$ revolves in a circle of radius $R$ at a constant speed $v.$ What is the ratio of the largest and smallest frequency detected by a detector $D,$ at rest, at a distance $2 R$ from the centre of the circle as shown in the figure? (take speed of sound in air as $C$)

A source of sound of frequency $f_1$ is placed on the ground. A detector placed at a height is released from rest on this source. The observed frequency $f( \mathrm{Hz})$ is plotted against time $t$ (s). The speed of sound in air is $300 \mathrm{m} {\mathrm{s}}^{-1}.$ Find $f_1\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right).$