If the pressure, temperature, and density of an ideal gas are denoted by $p, T$ and $\rho$, respectively, the velocity of sound in the gas is

An earthquake generates both transverse $S$ and longitudinal $P$ waves in the earth with speeds $4.5 \,km/s$ and $8.0 \,km/s$, respectively. $A$ seismograph records that the first $P$-wave arrives $3.5 \,min$ earlier than the first $S$-wave. From the seismograph, the epicentre of the earthquake is located at a distance of: (in $\,km$)

$A$ narrow sound pulse (for example,a short pip by a whistle) is sent across a medium.
$(a)$ Does the pulse have a definite $(i)$ frequency,$(ii)$ wavelength,$(iii)$ speed of propagation?
$(b)$ If the pulse rate is $1$ after every $20 \; s$,(that is,the whistle is blown for a split of a second after every $20 \; s$),is the frequency of the note produced by the whistle equal to $1/20$ or $0.05 \; Hz$?

$A$ student plotted the following four graphs representing the variation of velocity of sound in a gas with the pressure $P$. Which one is correct?

Explain which properties are necessary to understand the speed of mechanical waves.

$A$ man fires a bullet standing between two cliffs. The first echo is heard after $3 \, s$ and the second echo is heard after $5 \, s$. If the velocity of sound is $330 \, m/s$,then the distance between the cliffs is .... $m$