Finding Speed using Doppler Shift

[Toastminion]

Homework Statement

Light with a frequency of 6.1(10¹⁴) Hz is measured from a star known to produce light with a frequency of 6.0(10¹⁴). How fast is the star moving toward or away from earth?

Homework Equations

f = f₀(v + v_o)/(v-v_s.

f=observed frequency
f₀ = original frequency
v=wave speed
v_o = wave of observer
v_s=wave of source

The Attempt at a Solution

6.1(10¹⁴) = 6.0(10¹⁴)(3.0x10⁸ + 0)/(3.0x10⁸ + x)

-> (3.0x10⁸ + x) = 6.0(10¹⁴)(3.0x10⁸ + 0)/6.1(10¹⁴)

-> x = ( 6/6.1 x (3.0(10⁸) ) - 3.0x10⁸

-> -4918032.787 m/s
Moving away at 4918032.787 m/s

I feel that I'm doing it wrong since shouldn't it be moving toward Earth since the frequency observed is higher?

 

[NascentOxygen]

Your equation was: f = f0(v + vo)/(v-vs)
where vs is the speed towards the observer which gives that higher f.

You changed it, for some reason, and used +vs
which, to still be correct, means your vs is now the negative of its speed towards the observer.

You calculated this to be -4918032.787 m/s,
so take the negative of that and you have the speed towards the observer.

I haven't checked your arithmetic.