The more dense the air, the more lift is available for a wing. A properly shaped wing takes full advantage of normal air density.
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Yes, the overall density would be less than if the rod were pure metal.
An increase in air density will mean a decrease in the absorption and radiation of energy. An increase of air density causes temperature and pressure to rise.
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The higher the air density, the more oxygen available for combustion.
The density of air increases and then decreases as the sound wave passes.