# The Doppler Effect for Light Waves

• sameejane
In summary, the conversation discusses the question of at what wavelength a rocket cruiser's light detector would detect the red tail lights of a daredevil passing at a higher speed. The attempt at a solution involves using the dropper effect and relativistic velocity transformations, resulting in a wavelength of 801.2368685 nm. The conversation also mentions the need for two formulas to accurately calculate the Doppler shift at relativistic speeds.
sameejane

## Homework Statement

You are cruising to Jupiter at the posted speed limit of 0.1c when suddenly a daredevil passes you, going in the same direction, at 0.3c. At what wavelength does your rocket cruiser's light detecter "see" his red tail lights? Is this wavelength ultraviolet, visible, or infrared? Use 650 nm for the wavelength of red light.

## Homework Equations

I used the dropper effect for the light of a receding source"
√((1+vs/c)/(1-vs/c) * λo

## The Attempt at a Solution

I tried using 0.3c for the speed of the source, and 650 for λo. (I know the answer is 800 nm); I then tried using 0.1c instead. I got (almost) the right answer though when I plug in 0.2c... the wavelength came up as 796 nm.

Don't know what else to use!

Remember that the two cited speeds (and they should have been! ) are both with reference to Jupiter. It's not that you are observing the speeder going by you at 0.2c. Each has his own speedometer and those readings are 0.1c and 0.3c.

You need two formulas. One to give you the true relative speed between the two rocket ships and the other to compute the Doppler shift relativistically.

BTW I got 801.2368685 nm.

## What is the Doppler Effect for Light Waves?

The Doppler Effect for Light Waves is a phenomenon that occurs when the source of light waves and the observer are in relative motion. This causes a change in the frequency of the light waves perceived by the observer.

## How does the Doppler Effect for Light Waves work?

The Doppler Effect for Light Waves works by changing the frequency of the light waves based on the relative motion between the source and the observer. If the source is moving towards the observer, the frequency increases and the light appears bluer. If the source is moving away from the observer, the frequency decreases and the light appears redder.

## What is the difference between the Doppler Effect for Light Waves and the Doppler Effect for Sound Waves?

The main difference between the Doppler Effect for Light Waves and the Doppler Effect for Sound Waves is the medium through which the waves travel. Light waves travel through a vacuum, while sound waves require a medium, such as air or water. Additionally, the Doppler Effect for Light Waves is more pronounced, as the speed of light is much faster than the speed of sound.

## What are some real-life applications of the Doppler Effect for Light Waves?

The Doppler Effect for Light Waves has many practical applications, such as in astronomy for determining the speed and direction of celestial objects, in medical imaging for measuring blood flow, and in radar technology for tracking the movement of objects.

## What is the formula for calculating the Doppler Effect for Light Waves?

The formula for calculating the Doppler Effect for Light Waves is fobs = fsource x (c ± vobs) / (c ± vsource), where fobs is the observed frequency, fsource is the source frequency, c is the speed of light, vobs is the velocity of the observer, and vsource is the velocity of the source. The ± sign depends on whether the source is moving towards or away from the observer.

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