Speed of Sound in Ideal Gases: Variation & Derivation

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The speed of sound in an ideal gas varies with temperature, being directly proportional to the square root of the absolute temperature. The relationship is expressed by the formula c = √(kRT), where c represents the speed of sound, k is the ratio of specific heats, R is the ideal gas constant, and T is the temperature. Contrary to initial assumptions, the speed of sound is not directly proportional to the medium's density. Understanding this relationship is crucial for applications in aerodynamics and thermodynamics. The discussion emphasizes the importance of temperature in determining sound speed in gases.
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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:

c = \sqrt{k R T}

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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