How Does Temperature Affect the Speed of Sound?

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SUMMARY

The speed of sound in air is directly proportional to the square root of the absolute temperature. At 20 °C (293.15 K), the speed of sound is 343 m/s. To calculate the speed of sound at -10 °C (263.15 K), the correct formula is speed at -10 °C = 343 x √(263.15)/√(293.15), resulting in a speed of 324.92 m/s. The discussion emphasizes the importance of understanding proportionality in physics problems rather than calculating intermediate variables unnecessarily.

PREREQUISITES
  • Understanding of the relationship between temperature and the speed of sound
  • Knowledge of absolute temperature in Kelvin
  • Familiarity with square root calculations
  • Basic principles of proportionality in physics
NEXT STEPS
  • Study the derivation of the speed of sound formula in different gases
  • Learn about the effects of altitude on sound speed
  • Explore the relationship between temperature and sound speed in liquids
  • Investigate real-world applications of sound speed calculations in engineering
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Students studying physics, educators teaching thermodynamics, and professionals in acoustics or meteorology will benefit from this discussion.

chawki
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Homework Statement


The speed of sound in the air is proportional to the square root of the absolute temperature. At 20 °C the speed of sound is 343 m/s.

Homework Equations


What is the speed of sound at –10 °C? (0 °C = 273 K).


The Attempt at a Solution


speed of sound= x*\sqrt{}T
x*\sqrt{}293.15=343m/s
x=20.03

so the speed of sound at -10 C (263.15K) is: 20.03*\sqrt{}263.15 = 324.92m/s.
 
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hi chawki! :smile:

your answer is correct, and your method works, but it will lose you marks in the exam

you do not need to find the value of x …

the whole point of questions like this is to see whether you understand this point

you have done this in two steps: you found x, and then you eliminated x …

that is a waste of time (and introduces an opportunity for error)

the correct method (to be used in all "proportionality" cases) is:

speed at -10° C (263.17° K) = 343 x √(263.15)/√(293.15) = 324.92​
 
Ah the yellow fish again :P
Thank you for your help tiny-tim :)
I try to understand your method
 

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