Question

The speed of sound in air at $0^\circ C$ is nearly:

Answer 1

Hint: The speed of sound decreases with decrease in temperature. With every $1^\circ C$ change in temperature, the speed of sound decreases about $0.6m{s^{ - 1}}$. The speed of sound at room temperature ($20^\circ C$) is $343m{s^{ - 1}}$.

Complete step by step answer:
We know that the speed of sound at room temperature i.e. $20^\circ C$ will be $343m{s^{ - 1}}$. But it is not constant. It gets affected by the temperature of the medium. As we decrease the temperature, the speed of the sound also decreases. The reason for this decrease can be explained on the basis of thermodynamics. We know that sound cannot travel without a medium.

As the temperature decreases, the kinetic energy of the particles also decreases. Due to this decrease in the kinetic energy of the particles, the sound transferring capacity also decreases which in turn decreases the speed of sound.

We know that the speed of sound decreases by $0.6m{s^{ - 1}}$ with every $1^\circ C$ fall. The difference in temperature when the temperature falls from $20^\circ C$ to $0^\circ C$ is $19^\circ C$.
Thus the total speed decrease will be,
$ \Rightarrow 0.6 \times 19 = 11.4m{s^{ - 1}}$
The speed of sound at $0^\circ C$ will be,
$ \Rightarrow 343m{s^{ - 1}} - 11.4m{s^{ - 1}} = 331.6m{s^{ - 1}}$

Hence the speed of sound at $0^\circ C$ will be $331.6m{s^{ - 1}}$.

Note: The speed of sound depends on various properties of the given medium. The speed of sound is higher in solids as compared to liquid and gas. The speed of sound decreases with a decrease in temperature. The speed of sound is more in medium with lower atomic mass particles as compared to the speed in higher atomic mass particles. The speed of sound also has a slight dependence on the humidity of the gaseous medium. For a gaseous medium, the speed of sound depends on pressure and density also.