Question

Arrange the following in ascending order of the speed of sound in them.
(i) Water.
(ii) Steel.
(iii) Nitrogen.
A. (iii),(ii),(i)
B. (i),(iii),(ii)
C. (iii),(i),(ii)
D. (ii),(i),(iii)

Answer 1

Hint: Sound is a longitudinal wave. Because the particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves. So sound waves produce disturbance in the medium which when hits the eardrum is interpreted as sound. Unlike matter the waves travel better in denser materials or denser medium, because in denser medium the particles are more packed and any disturbance will travel more easily in denser medium.

Complete step-by-step answer:
The speed of sound is mainly affected by two factors. One is the medium in which it travels and the temperature. Speed of sound is more in a denser medium . between steel, water and nitrogen gas the most denser medium is steel, below that water and the lowest denser medium is nitrogen. So the speed of sound in steel will be maximum then water medium then nitrogen medium. So the ascending order of velocity of sound is nitrogen < water < steel.
So the correct option is C. (iii), (i), (ii)

So, the correct answer is “Option C”.

Additional Information: Speed of sound in fluid(liquid or gas): In a longitudinal wave, the particles of the medium oscillate forward and backward in the direction of propagation of the wave. They cause compression and rarefactions of small volume elements of fluid. So the speed of a longitudinal wave through fluid is determined by two factors:
(i) The volume elasticity or bulk modulus $\kappa$ of it is fluid.
(ii) The density of the fluid which determines its inertia.
So using dimensional calculation we can get the speed of sound in a fluid medium is
$v=\sqrt{\dfrac{\kappa }{\rho }}$
Speed of sound in a solid: The speed of sound through a solid of bulk modulus $\kappa$, modulus of rigidity $\eta $ and density $\rho$ is given by
$v=\sqrt{\dfrac{\kappa +\dfrac{4}{3}\eta }{\rho }}$
If $Y$ is the young’s modulus of the solid then the velocity of sound is given by
$v=\sqrt{\dfrac{Y}{\rho }}$

Note: The first theoretical formula for velocity of sound in air was given by Einstein. He considered that the sound wave travels in air under isothermal conditions (i.e. during propagation of sound the medium will not heat up). But his formula gave the result which was $15\%$ less than the experimental value. So Laplace corrected Newton’s formula and considered the traverse of sound waves in gas to be in adiabatic condition (no heat exchange). Which gave a more accurate result.
Speed of sound in water is $1480m{{s}^{-1}}$
Speed of sound in air is $343m{{s}^{-1}}$
Speed of sound in steel is $5920m{{s}^{-1}}$.