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

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Homework Help Overview

The original poster is attempting to calculate the air temperature based on the time difference between seeing fireworks and hearing the sound, using the speed of sound formula. The problem involves understanding the relationship between sound speed, temperature, and the constants associated with air.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the constants needed for the calculations, such as gamma, R, and the effective molecular mass of air. There is also a mention of a specific equation for temperature derived from sound speed, which some participants question regarding its origin and validity.

Discussion Status

Some participants have provided links to resources that explain the constants and equations involved. There is an ongoing exploration of the assumptions behind the problem and the specific values used in the calculations, but no consensus has been reached on how to proceed with the solution.

Contextual Notes

There is a noted emphasis on the precision of the time measurement, with one participant commenting on the unusual number of significant figures provided in the problem statement. This may influence how participants approach the calculations.

BuBbLeS01
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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?
 
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BuBbLeS01 said:
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. :rolleyes:

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!
 
Last edited by a moderator:
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?
 
BuBbLeS01 said:
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.
 
oh yea I am sorry I didn't scroll down.
 
can someone please help me?
 

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