Temperature and Sound Wave Velocity: Exploring the Proportional Relationship

[TP9109]

Apologies if this is a question with a basic answer, I'm coming back to physics after many years of being away from it! I read somewhere that for longitudinal sound waves traveling through air, if the temperature increases by 1 degree celsius then the velocity of the wave will increase y 0.6 m/s. They back this up by saying it is because v is proportional to sqrt of T, T in Kelvin. I don't understand this as if you square root the temp at 70 degrees and then square root the temp at 71 degrees, the difference between the two resulting numbers will be smaller than if the two temps were lower numbers e.g 30 and 31. So how can going from 70 to 71 degrees increase the velocity by the same amount as going from 30 to 31 as there is a square root involved giving smaller differences at changes in higher temperature values and larger differences between changes in lower temp values, so how can they say that the velocity increases by 0.6 m/s per degree regardless of whether a small or large temperature is involved?
Thanks for any help

 

[russ_watters]

Apologies if this is a question with a basic answer, I'm coming back to physics after many years of being away from it! I read somewhere that for longitudinal sound waves traveling through air, if the temperature increases by 1 degree celsius then the velocity of the wave will increase y 0.6 m/s. They back this up by saying it is because v is proportional to sqrt of T, T in Kelvin. I don't understand this as if you square root the temp at 70 degrees and then square root the temp at 71 degrees, the difference between the two resulting numbers will be smaller than if the two temps were lower numbers e.g 30 and 31. So how can going from 70 to 71 degrees increase the velocity by the same amount as going from 30 to 31 as there is a square root involved giving smaller differences at changes in higher temperature values and larger differences between changes in lower temp values, so how can they say that the velocity increases by 0.6 m/s per degree regardless of whether a small or large temperature is involved?
Thanks for any help

It's an approximation that is valid only for a range of temperatures:
https://en.wikipedia.org/wiki/Speed_of_sound#Practical_formula_for_dry_air

 

[TP9109]

I missed that part of the wiki page when I was googling answers, thanks for that it makes sense now