Speed of Sound in Ideal Gases: Variation & Derivation

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Discussion Overview

The discussion centers on how the speed of sound varies with temperature in an ideal gas and the derivation of this relationship. It includes theoretical considerations and mathematical reasoning related to the properties of gases.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant inquires about the relationship between the speed of sound and temperature in an ideal gas, seeking a derivation of this relation.
  • Another participant suggests that the speed of sound is directly proportional to the medium's density, indicating a possible misunderstanding of the relationship.
  • A later reply acknowledges a previous error in reasoning and provides a link to additional information on the topic.
  • One participant presents a formula for the speed of sound, stating it is proportional to the square root of the absolute temperature, along with the relevant constants.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the relationship between speed of sound and density, and there are competing views regarding the derivation of the speed of sound in ideal gases.

Contextual Notes

Some assumptions about the ideal gas behavior and the specific heat ratio may not be fully addressed, and the implications of density on the speed of sound remain unresolved.

benitta
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how does the speed of sound vary with temperature in an ideal gas? how do we derive this relation?
 
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Isn't the speed of sound directly proportionate to the medium's density?
 
The speed of sound is proportional to the square root of the absolute temperature:

[tex]c = \sqrt{k R T}[/tex]

where:
c = speed of sound
k = ratio of specific heats (1.4 for air)
R = Ideal gas constant
T = Temperature
 
thanks guys...
 

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