Question

In gases, the speed of sound is inversely proportional to ______ of the density when other factors are the same.

Options

A
Square root
B
Square
C
Third power
D
Third root

Explanation

Speed of sound (v) in gas is directly proportional to square root of isothermal elasticity (K) i.e. compression-rarefaction under constant temperature, and inversely proportional to square-root of density (ρ)
This is given by Newton’s formula,
V = √ (k/ρ).
therefore , from the formula it can be seen that
v=√ (1/ρ)
Hence, speed of sound is inversely proportional to square root of the density.

a) Square root: This is the correct option. The speed of sound in a gas is inversely proportional to the square root of the density when other factors (such as pressure and temperature) are kept constant. Mathematically, this relationship can be represented as:
Speed of sound ∝ 1/√density

b) Square: This option is not correct. The speed of sound is inversely proportional to the square root of the density, not the square of the density.

c) Third power: This option is not correct. The speed of sound is inversely proportional to the square root of the density, not the cube of the density.

d) Third root: This option is not correct. The speed of sound is inversely proportional to the square root of the density, not the cube root of the density.