What factors affect the velocity of sound?

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    Sound Velocity
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The velocity of sound is influenced by the medium's pressure and density, remaining constant at high altitudes if air composition is unchanged. While radiation pressure does not affect sound velocity, temperature significantly impacts it. Sound travels faster in denser mediums like water and solids compared to air. Additionally, excess CO2 can alter the pitch of instruments, despite the sound velocity remaining stable. Understanding these factors is crucial for comprehending sound propagation in various environments.
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We know that the velocity of sound has relation with the pressure of the medium.
And I'm wondering wether it has relation with the pressure of radiation ?
Thanks!
 
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I recently heard a clarinet solo at an elevation of about 9000 feet, and wondered why the pitch had not changed. The velocity of sound depends on the square root of the ratio of air pressure over air density. Thus the velocity of sound remains constant, even at high altitude, as long as the composition of air remains constant. However, excess
CO2 concentration from an overzeleous musician can detune the instrument. Radiation pressure (electromagnetic radiation) is entirely different, and has no direct relation to the velocity of sound (pressure waves in the medium).
 
SqRt of stiffness/density.
Which is why sound travels faster in water than air, and even faster in solids.
Also highly dependent on temperature.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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