Question

Sound travels with different speeds in the medium. In what order does the velocity of the sound increase in these media.
a) Water, iron and air
b) Iron, air and water
c) Air, water and iron
d) Iron, water and air

Answer 1

Hint: The speed of the sound in any medium depends on the two factors. One is the density of the medium and the other is the stiffness. First we will see how the speed of the sound depends on these factors and accordingly obtain the order of increase in the velocity of the sound as per the alternatives provided.

Formula used: $v=\sqrt{\dfrac{B}{\rho }}$

Complete step by step answer:
Let us say we wish to calculate the speed of sound in a particular medium. If the density of the medium is ‘$\rho $’ and that its bulk modulus is ‘B’, then the speed of light ‘v’ is given by,
$v=\sqrt{\dfrac{B}{\rho }}$
For most of the solids the bulk modulus is very high as well as the density of the solids. But the extent to which the bulk modulus of a solid like iron is so huge that the density of the substance in terms of bulk modulus is very less. The order of the bulk modulus for iron, water and air can be written as,
Iron>water> air.
The density of the above substances can be ignored as they don’t play much role. Hence we can conclude that the speed of sound in the above substances in the increasing order can be written as,
air, water and iron.

So, the correct answer is “Option c”.

Note: The answer to the above question can also be approached in this way. Sound is nothing but the disturbance in the medium. If the particles of the medium are close to one another we can say that the sound will propagate faster. Hence, accordingly we will get the required answer.