AAMC 4 #15 Doppler Effect

[UTPHS]

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An astronomer observes a hydrogen line in a spectrum of a star. The wavelength of hydrogen in a laboratory is 6.563E-7 but the wavelength of the star's light is measured at 6.56186E-7. Which of the following explains this discrepancy?

1) The star is approaching Earth
2) The star is moving way from Earth

My logic: Since the wavelength of the detector (laboratory) is larger than the wavelength of the source (star in space), that means the frequency of the detector is smaller than the frequency of the source. => A smaller frequency would mean the star is moving away from the earth while a larger frequency would mean the star is approaching the earth, so the answer would be #2.

Did I make a simple mistake somewhere? What's wrong with my reasoning?

 

[karafox]

wavelength of observer > wavelength of source
frequency of observer < frequency of source

doppler effect equation: frequency of observer = frequency of source (v ± v_observer / v ± v_source)

v_observer = 0

because frequency of observer < frequency of source, then (v / v ± v_source) should be a value smaller than 1. in other words, the sign in the denominator should be "+" which represents the source is approaching the observer.

 

[rjosh33]

An astronomer observes a hydrogen line in a spectrum of a star. The wavelength of hydrogen in a laboratory is 6.563E-7 but the wavelength of the star's light is measured at 6.56186E-7. Which of the following explains this discrepancy?

1) The star is approaching Earth
2) The star is moving way from Earth

My logic: Since the wavelength of the detector (laboratory) is larger than the wavelength of the source (star in space), that means the frequency of the detector is smaller than the frequency of the source. => A smaller frequency would mean the star is moving away from the earth while a larger frequency would mean the star is approaching the earth, so the answer would be #2.

Did I make a simple mistake somewhere? What's wrong with my reasoning?

Ok, I think I see where you went wrong. The wavelengths given in the question stem refer to two different measurements of the wavelength. That is, it's not starting out at 656.186 nm and being detected at 656.3 nm. Rather, the 656.3 nm wavelength is the wavelength of hydrogen under normal (non-moving) conditions -- its your reference value. Light from the star is then being detected at 656.186 nm, making the detected wavelength smaller than the reference value.

As you noted above, smaller wavelength means larger frequency. So, the light from the star has a larger frequency than normal, meaning it has to be moving toward its detector, which is, of course, on Earth.

 

[going2breakdown]

This question is all about the qualitative not the quantitative. Light is a wave right (okay it has a wave and particle duality but just assume it as a wave here). If the star moves towards the earth the wavelengths will shorten right? In the direction of motion waves "scrunch" closer together. So, it the star is moving towards you, the distance between the waves are going to shorten (doppler effect, but with light!), and therefore the frequency will increase (shorter wavelength) according to you. This is how we know if a star is moving towards us or away from us in space just fyi. If it red shifted (moving away) or blue shifted (moving towards us).