The time period of a simple pendulum is given by the formula, $T=2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$, where $T=$ time period, $l=$ length of pendulum and $g=$acceleration due to gravity.

If the length of the pendulum is decreased to $\frac{1}{4}$ of its initial value, then what happens to its frequency of oscillations?

A police targets a thief, who is at rest at point $Q$. He fires a bullet from a point $P$ which is at a distance of $990 \mathrm{m}$ from $Q$ and it reaches the point $Q$ in $3 \mathrm{s}$. When the bullet is fired at $P$ it produced a sound, which was heard by the thief. What is the difference in time taken by the sound and the bullet to reach point $Q$. Will the thief be able to escape from the bullet fired by police? Take the velocity of sound in air as $330 \mathrm{m} {\mathrm{s}}^{-1}$.

The flash of lightning, produced at a distance of $10 \mathrm{km}$ above the ground level is seen much before hearing the thunderbolt. Find the time gap between the two events observed by a person on the ground if the time taken by the lightning to reach the surface of the earth is negligible.

(velocity of sound $=330 \mathrm{m} {\mathrm{s}}^{-1}$ and velocity of light $=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$).

List the following persons in ascending order, according to the shrillness in their voice.

(a) A woman of age $40$

(b) A man of age $40$

(c) A $5 \mathrm{th}$ class girl

(d) An infant baby