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The temperature at which the speed of the sound in air becomes double of its value at 27 degree celsius is

The temperature at which the speed of the sound in air becomes double of its value at 27 degree celsius is

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1 Answers

Arun
25750 Points
5 years ago
Use the formula 
velocity of sound waves v = sqrt (P/rho) 

P is the pressure and rho is the density.Write this as 

v1 = root(p1/rho) 
v2= root (p2/rho) 

square both sides 

v1^2 = p1 /rho 

v2^2 = p2/rho 

Take the ration 

v1^2/v2^2 = p1/p2 

Put the values v1=1 and v2 = 2 

YOu get 

1/4 = p1/p2 

p1 = n kb T1 and p2= n kb T2. Here n is the number density. kb Boltzmann constant and T1 and T2 are temperatures. 

If you use it in the above equation you get 

T2= 4 T1 

T1 is 27 degrees= 273 + 27 = 300 

T2= 1200 degrees = 1200-273 = 927 degrees.

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