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No. The speed of sound in air depends only on the temperature of the gas. Sound is a vibration that spreads as a wave through particles, such as those in air. Temperature is a measure of how energetic those particles are, hence, how fast they are moving. The more energetic the air particles are, the faster sound waves travel through the air. If the pressure of the air around you were to double, but the temperature remained the same, the speed of sound would stay the same.