Speed of Sound & How our environment affects it.

Ever wondered in childhood why the thunder struck always after the lightning. Well we grew up to knew that sound travels slower than light ( Big deal “Light”,get over it).

Then came 9^th standard Physics & we all learned that sound travels with the speed of 342 m/sec. ( made us feel like a bit of Einstein, when we would tell our folks back home about speed of sound).

Now, for those of you who were happy with that fact, please stop here. No, seriously. Coz the next few para’s is gonna leave more confused than depressed.

Without much haggle, I’m gonna delve into the topic of how the speed of sound varies with humidity and Temperature.

Yes Sir, you read that correct. The speed that we thought was constant varies with the ever impressing factors of temperature and Humidity.

Now, many of you would have started checking on Google for the formula for the speed of sound & those of you already aware with the formula, know that the speed of Sound is defined by the formula:

Where  c: Speed of sound, P : Ambient Pressure & p: Gas Density

ᵧ as we know is the term dependent upon the freedom of the gaseous molecule. Since air is made up of diatomic molecules, the value of ᵧ is taken to be 1.41.

Thus our equation becomes  

So, how does temperature plays any role in determining the velocity of sound at all. Well, we use the equation of state of air of an ideal gas, which is PV= RT .

p is density ( mass per unit volume) in the equation, from which we derive the following :  

                              

Where R: Universal Gas constant, T: Absolute Temperature, M: Mean molecular weight of gas at sea level.

Since the values of R & M are constant, the velocity of sound maybe shown as temperature dependant as follows:

Where T: temperature in Kelvin , c (0): Reference speed of sound under defined conditions.

Thus, the speed of sound is seen to increase as the square root of absolute temperature.  Hence converting the same in centigrade we get,

where t: temperature in degree Celsius

Now, many will be asking them self that does'nt pressure any way affect the velocity. The answer to that is, that change in pressure indeed affects change in density of the air, but the inverse is not true. Change in density of air does not affects the change in pressure. Thus, there is no change in the velocity of sound due to any change in the density of air around it.