# Factor Affecting Speed of Sound in Gas or Air Medium

There are different factors that affect the speed of sound in gas or air medium. Some of the major factors are given below:

Effect of pressure (P)

When pressure (P) of a gas is increased, its velocity also increases and vice versa. As a result, the ratio of p/ ρ remains constant. So, by relation,

${\text{V}} = \sqrt {\frac{ \gamma P}{ \rho}} = \text{Constant}$

Effect of temperature (T)

Since, PV = RT  for 1 mole gas, we have the following equation,

$${\text{V}} = \sqrt {\frac{ \gamma \text{RT}}{ M}}$$

On keeping γ and m constant,

$$V \propto \sqrt {\text{T}}$$

Sp, the velocity of sound in gas is directly proportional to the square root of the temperature in Kelvin scale.

If we have two velocities V1 and V1 having different temperature T1 and T2, Then:

$$\text{V}_1 \propto \sqrt {\text{T}_1}……(i)$$

$$\text{V}_2 \propto \sqrt {\text{T}_2}……(i)$$

From equation (i) and (ii), we get:

$$\frac{\text{V}_1}{\text{V}_2} = \sqrt \frac{\text{T}_1}{\text{T}_2}$$

Effect of density (ρ)

By relation: $${\text{V}} = \sqrt {\frac{ \gamma P}{ \rho}}$$

Keeping γ and P constant,

$${\text{V}} \propto \sqrt {\frac{ 1}{ \rho}}$$

So, velocity of sound in gas is inversely proportional to square root of density of gas.

Effect of molar mass

We have, $${\text{V}} = \sqrt {\frac{ \gamma \text{RT}}{ M}}$$

Keeping γ and T constant,

$${\text{V}} \propto \sqrt {\frac{ 1}{ \text{M}}}$$

Effect of wind

If air is blowing, speed of sound changes. If the wind blows in the direction in which the sound is travelling, the velocity of sound increases. If the direction of wind is opposite to the direction of sound, the velocity of sound gets decreased. Therefore the new velocity of sound becomes (v ±vw), where v is the velocity of sound and vw is the velocity of wind. If the sound makes an angle θ with the direction of sound, the component in the direction of sound is vwcos θ. So, the net velocity becomes v + vwcos θ.

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