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If gravity at a place increases or decreases, does it affect the sound wave propagating through that place. If for certain place gravity increases on earth will there be change in direction or wavelength of the sound wave.

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Changes in gravity will lead to changes in air pressure and density. Their effect on speed of sound cancel each other out in an ideal gas, but since air is not an ideal gas, the speed of sound will change. Unfortunately, it is hard to say in which direction the change will go because the direction also depends on humidity; see here Speed of Sound in Air.

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