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

  • A
    Option A
  • B
    Option B
  • C
    Option C
  • D
    Option D

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If the temperature of the atmosphere is increased,which of the following characteristics of a sound wave is affected?

At what temperature (in $^\circ C$) will the speed of sound in air be $3$ times its value at $0^\circ C$ (in $^\circ C$)?

The velocities of sound at the same pressure in two monatomic gases of densities ${\rho _1}$ and ${\rho _2}$ are $v_1$ and $v_2$ respectively. If ${\rho _1}/{\rho _2} = 2$,then the value of $\frac{{{v_1}}}{{{v_2}}}$ is:

Regarding the speed of sound in a gas, match the following:
$A$. Temperature of gas is made $4$ times and pressure $2$ times$P$. Speed becomes $2\sqrt{2}$ times
$B$. Only pressure is made $4$ times without change in temperature$Q$. Speed becomes $2$ times
$C$. Only temperature is changed to $4$ times$R$. Speed remains unchanged
$D$. Molecular mass of the gas is made $4$ times$S$. Speed becomes half

The Earth has a radius of $6400 \ km$. The inner core of $1000 \ km$ radius is solid. Outside it,there is a region from $1000 \ km$ to a radius of $3500 \ km$ which is in a molten state. Then again from $3500 \ km$ to $6400 \ km$,the Earth is solid. Only longitudinal $(P)$ waves can travel inside a liquid. Assume that the $P$ wave has a speed of $8 \ kms^{-1}$ in solid parts and of $5 \ kms^{-1}$ in liquid parts of the Earth. An earthquake occurs at some place close to the surface of the Earth. Calculate the time after which it will be recorded in a seismometer at a diametrically opposite point on the Earth if the wave travels along the diameter.

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