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This can be answered using light or sound. Light will remain at a constant speed regardless of frequency or amplitude. Its shift in frequency (Doppler shift) is caused by the extreme distances the light had to travel to get here. Still it remains at the same speed. Sounds speed will change with local conditions. Also subject to an audible Doppler shift when a constant note is moved past you you can hear the pitch shift. The motion compresses the sound as it approaches and spreads it out as it moves away from you.

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