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"760. An interstellar gas circles the core of earth's galaxy. If the wavelength of the light reflecting off the gas coming toward the earth is 499 nm, and the wavelength of light reflecting off the gas moving away from earth is 501 nm, what is the speed of the gas?

A. 4.2xl0^4 m/s

B. 1.2xl0^5 m/s

C. 6.0xl0^5 m/s

D. 1.5xl0^11 m/s

760. C is correct. The relative velocities of the gas moving away from the earth and the gas moving toward the earth are equal and opposite; therefore the change in wavelength must be the same for both but in opposite directions, and the wavelength of light coming from earth must be 500 nm. Now use the Doppler approximation: vic= (change in wavelength)/ (wavelength of source).. v/(3x10^8) = 1/500. This velocity must be divided by 2 because the change in the distance of the path traveled by the light is decreased or increased by a factor twice the velocity of the gas. To visualize this, notice that the box below travels toward the man at 1 rn/s. However, the path of light going to the box and back to the man changes from 20m to 18m in a second, or 2 rn/s. This division by 2 is required here because the source is also the observer, and the wave is making a round trip."

Did EK take the average of the two wavelengths? I think it is accounting for the relative velocities of the gas. The gas is slowing down and speeding up the light waves, right? Shouldn't the change in wavelength be 2 m/s instead.

In addition, why are they saying that the velocity should be divided with two? I don't get their box analogy. In addition, if I solve for the equation v/(3x10^8) = 1/500. I get v= 6.0xl0^5 m/s without dividing by 2 unless my math is wrong somehow.

Anyways, if you have any ideas please let me know. I want to finish this section of my MCAT studying and move on.

Thank you for all your help.

Verónica