Courses
Courses for Kids
Free study material
Offline Centres
More
Store

At what temperature, speed of sound in air will be doubled than its speed in air at STP?

Last updated date: 16th Jun 2024
Total views: 344.9k
Views today: 4.44k
Verified
344.9k+ views
Hint: Speed of a longitudinal wave when propagating in air is directly proportional to the temperature of air at the time of wave propagation. Sound is also a longitudinal wave, and it's on-book speed which is $343m{s^{ - 1}}$, is recorded at STP $(0^\circ C,1atm)$ .

Sound waves are longitudinal waves. Their speed of propagation is related to the absolute temperature of the atmosphere by the following relation.
$v \propto \sqrt T$
Where, $v$ is speed of sound
$T$ is absolute temperature ( measured in Kelvin scale)
Now let us look at the problem.
Let us assume that at standard temperature and pressure or at temperature ${T_1}$, speed of sound is ${v_1}$
Let ${v_2}$ is the doubled spee$\Rightarrow {T_2} = 1092K$d of sound at temperature ${T_2}$. $({v_2} = 2{v_1})$
As we know, speed of sound is directly proportional to the square root of temperature, we can write
${v_1} \propto \sqrt {{T_1}}$ ……….. (1)
And ${v_2} \propto \sqrt {{T_2}}$ ………. (2)
Now, $\dfrac{{{v_1}}}{{{v_2}}} = \sqrt {\dfrac{{{T_1}}}{{{T_2}}}}$
Substituting the value of ${v_2}$ in the above equation, we get,
$\Rightarrow \dfrac{1}{2} = \sqrt {\dfrac{{{T_1}}}{{{T_2}}}}$
At STP, ${T_1}$ is $273K$
So, $\Rightarrow \dfrac{{273}}{{{T_2}}} = \dfrac{1}{4}$
${T_2} = 1092K$

So, the answer is, at $1092K$ or $819^\circ C$, the speed of sound will be double the value of its speed at STP.

Notes: Sound travels at a speed of $340m{s^{ - 1}}$ at STP. Speed of any longitudinal wave depends on its media of propagation, if the media allows fast propagation, the wave will do so. By increasing the temperature of the medium, one can achieve a speed increase of sound waves. It is directly proportional to square root of the absolute temperature of the media. At $819^\circ C$ we can achieve the doubled speed of sound, but practically it is not possible in day to day life.