A spaceship is approaching a space station at a speed of 1.8 ×10^5 m / s . The space station has

step 1 We know the space station and the ship are moving towards one another. So the frequency after be

A spaceship is approaching a space station at a speed of 1.8...

A spaceship is approaching a space station at a speed of $1.8 \times$ $10^{5} \mathrm{m} / \mathrm{s}$ . The space station has a beacon that emits green lightwith a frequency of $6.0 \times 10^{14} \mathrm{Hz}$ (a) What is the frequency of the beacon observed on the spaceship? (b) What is the change in frequency? (Carry five digits in these calculations.)

A spaceship is approaching a space station at a speed of $1.8 \times$ $10^{5} \mathrm{m} / \mathrm{s}$ . The space station has a beacon that emits green lightwith a frequency of $6.0 \times
10^{14} \mathrm{Hz}$ (a) What is the frequency of the beacon observed on the spaceship? (b) What is the change in frequency? (Carry five digits in these calculations.)

Key Concepts

Frequency

Frequency, measured in Hertz, is a key parameter in understanding wave phenomena. It represents the number of cycles or oscillations that occur in a unit of time and is directly related to the energy of the wave. In problems involving wave motion, any change in the observed frequency is a central piece of evidence that there is relative motion between the source and the observer.

Speed of Light

The speed of light is a fundamental constant of nature, approximately 3 × 10^8 meters per second, which plays a central role in the equations of electromagnetism and special relativity. In the context of the Doppler shift for light, it serves as the reference for determining how large the effects of motion will be on the observed frequency.

Doppler Effect

The Doppler Effect is the phenomenon in which the frequency of a wave changes due to the relative motion between the source and the observer. This fundamental concept applies to all types of waves, including sound and electromagnetic waves, and explains why an observer moving toward a wave source perceives a higher frequency while moving away results in a lower frequency.

Relativistic Doppler Shift

For electromagnetic waves, especially when dealing with high speeds, the relativistic Doppler shift must be used to account for the effects of time dilation. The relativistic formula modifies the classical Doppler effect to ensure that the invariance of the speed of light is maintained, providing an accurate description even when the relative velocity is a significant fraction of the speed of light.

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