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The air pressure has no effect.

The static air pressure p_ and the density ρ of air (air density) are proportional at the same temperature. The ratio p_ / ρ is always constant, on a high mountain or even on sea level altitude.

That means, the ratio p_ / ρ is always constant on a high mountain, and even at "sea level". The static atmospheric pressure p_ and the density of air ρ go always together. The ratio stays constant.

When calculating the speed of sound, forget the atmospheric pressure, but look accurately at the very important temperature. The speed of sound varies with altitude (height) only because of the changing temperature there.

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