Calculate Air Temperature for 4th of July Fireworks Using Speed of Sound Formula

[BuBbLeS01]

Test On Monday...please help!

Homework Statement

My home is exactly 7.8 km from the Stadium where the 4th of July fireworks are held. The time difference between when I see a flash and when I hear the corresponding sound is 22.4073542085608 s. What is the temperature (in degrees Celsius) of the air?

Homework Equations

Vsound = sqrt (GAMMA * R * T) / M

The Attempt at a Solution

T = 20 degrees Celsius + 273 = 293
V = 7800/22.4073542085608 = 348.1 m/s

T = Vsound^2 * M / GAMMA * R

But I don't know M, GAMMA, or R?

 

[Astronuc]

Gamma and R are constants, and M is the effective molecular mass.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html

"R = universal gas constant = 8.3145 J/mol K"

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html

\gamma = C_P/C_V

For air M must be weighted according to the fractions of N2 and O2.
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/barfor.html#c6

 

[Doc Al]

The time difference between when I see a flash and when I hear the corresponding sound is 22.4073542085608 s.

With 16 significant figures, whoever devised this problem has a sense of humor.

Nonetheless...

R is a universal constant; gamma and M are constants specific to air. Read all about it here: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html#c1"

Astronuc beat me to it!

 

[BuBbLeS01]

lol I know I love the 16 sig figs. So I understand that...but she showed us this way...
T = ((vsound - 331 m/s) / 0.6 m/s) °C
= ((348.1 m/s - 331 m/s) / 0.6 m/s) °C
= 28.5 °C

And I am don't know where she got that equation and some of the numbers from?

 

[Doc Al]

And I am don't know where she got that equation and some of the numbers from?

The link I provided derives that exact equation.

 

[BuBbLeS01]

oh yea I am sorry I didn't scroll down.

 

[BuBbLeS01]

can someone please help me?