You are trying to communicate with a spaceship that is...

You are trying to communicate with a spaceship that is traveling at $1.2 \times 10^{8} \mathrm{m} / \mathrm{s}$ away from Earth. If you send a message at a frequency of $55 \mathrm{kHz}$, to what frequency should the astronauts on the ship tune to receive your message?

Key Concepts

Doppler Effect

The Doppler effect is a shift in the frequency (or wavelength) of a wave as perceived by an observer moving relative to the wave source. In communication, if the source or receiver is in motion, the signal will appear to have a higher frequency (blueshift) if moving closer, or a lower frequency (redshift) if moving away.

Relativistic Doppler Shift

When dealing with velocities that are a significant fraction of the speed of light, the classical Doppler formula no longer suffices. Relativistic Doppler shift incorporates the principles of special relativity, such as time dilation, to accurately describe the change in frequency of electromagnetic waves due to high-speed motion.

Frequency Tuning in Communications

Frequency tuning is the process of adjusting the receiver's frequency to align with the incoming signal's frequency. This adjustment is crucial in scenarios where the signal's original frequency has been shifted due to relative motion between transmitter and receiver, ensuring that the communication remains clear and effective.

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