Why Does the Observed Frequency Increase When a Galaxy Approaches?

[djerry]

Homework Statement

Atomic hydrogen emits a characteristic spectral line with a frequency of 1421 MHz. A radio
telescope observes this line in a certain galaxy at a frequency of 1432 MHz.
Is the galaxy approaching or receding, and at what speed (in km/s)?

Homework Equations

The Attempt at a Solution

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I assume the galaxy is approaching as the waves tend to bunch up and thus the perceived frequency is actually higher than the actual frequency. To find the speed I tried calculating the change in wavelength as true-observed and got 0.0016m. Using this fact I used the equation:

recession velocity/wave speed = change in wavelength/actual wavelength

And got a value of 0.007579, which my text says should be the fraction of the speed of light which the galaxy is approaching at. However, this value is positive and I'm told it should be negative if approaching! Where am I going wrong?

Thanks in advance.

 

[Doc Al]

However, this value is positive and I'm told it should be negative if approaching! Where am I going wrong?

What's the change in wavelength? Is the wavelength getting bigger or smaller?

 

[djerry]

The wavelength observed was smaller, which implies the object is moving toward the observer.

 

[djerry]

I calculated the change in wavelength as 0.2111m-0.2095m=0.0016m.

 

[Doc Al]

The wavelength observed was smaller, which implies the object is moving toward the observer.

Good.

If something gets smaller, is its change positive or negative?

 

[djerry]

Well it should be negative. But when you calculate you get a positive as you're taking a smaller number (the observed) from the true wavelength. Do I just assign a negative because it's getting smaller?

 

[Doc Al]

Well it should be negative. But when you calculate you get a positive as you're taking a smaller number (the observed) from the true wavelength. Do I just assign a negative because it's getting smaller?

It is negative. Note that change is defined as final - initial (or new - old), which is observed wavelength minus true wavelength.