You are trying to communicate with a rocket ship that is...

You are trying to communicate with a rocket ship that is traveling at $1.2 \times 10^{8} \mathrm{m} / \mathrm{s}$ away from Earth on its way into space. If you send a message at a frequency of $55 \mathrm{kHz},$ to what frequency should the astronauts tune to receive your message? [Hint: Use the result derived in Problem 80.]

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Key Concepts

Relativistic Doppler Effect

The relativistic Doppler effect describes how the observed frequency of electromagnetic waves changes when there is a relative motion between the source and the observer at speeds close to the speed of light. Unlike the classical Doppler effect, it incorporates time dilation and requires using Lorentz transformations, leading to formulas that involve the square root of ratios like (1 - v/c) and (1 + v/c).

Special Relativity

Special relativity is the framework that governs physics at high velocities, where speeds are a significant fraction of the speed of light. It introduces key modifications to our understanding of time and space, providing the basis for the relativistic Doppler effect by ensuring that the speed of light remains constant in all inertial frames.

Wave Frequency and Signal Transmission

The frequency of a wave is a measure of how many oscillations occur per unit time. In the context of signal transmission, any relative motion between the transmitter and the receiver alters the perceived frequency due to the stretching or compressing of the wavefronts, which is essential in calculating the correct tuning frequency for communication.

Transcript

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