Doppler Effect Source Moving Closer

[JSGandora]

Homework Statement

Superman is carrying a red lantern with wavelength 650nm. He flies toward you at a speed of 2.7x108 m/s.
What is the observed wavelength?

Homework Equations

$f'=\frac{f}{\left(1-\frac{v_s}{v}\right)}$
and
$f=\frac{c}{\lambda}$

The Attempt at a Solution

I used the equation $f'=\frac{f}{\left(1-\frac{v_s}{v}\right)}$ and got my answer to be $65$ nm. What did I do wrong?

 

[DaveC426913]

Homework Statement

Superman is carrying a red lantern with wavelength 650nm. He flies toward you at a speed of 2.7x108 m/s.
What is the observed wavelength?

Homework Equations

$f'=\frac{f}{\left(1+\frac{v_s}{v}\right)}$
and
$f=\frac{c}{\lambda}$

The Attempt at a Solution

I used the equation $f'=\frac{f}{\left(1+\frac{v_s}{v}\right)}$ and solved for $v_s$ and got my answer to be $75\times 10^8$ m/s. What did I do wrong?

Well, for starters, the result you provided is a velocity (m/s), when in fact, what was asked for was a distance(m) (of a wavelength).

 

[JSGandora]

OOPS, I accidentally copied the wrong thing. I actualy got 65 nm for the wavelength using the correct formula with the minus sign in the denominator, not plus sign (edited original post). Sorry about that.

 

[berkeman]

OOPS, I accidentally copied the wrong thing. I actualy got 65 nm for the wavelength using the correct formula with the minus sign in the denominator, not plus sign (edited original post). Sorry about that.

So can you now do your other question thread for the source moving away?

https://www.physicsforums.com/showthread.php?t=546027

.

 

[JSGandora]

Bleh, I also forgot to mention that the answer key said 149nm.

Sorry for not giving all the information, I made this all a big mess. I don't understand why the answer is 149nm, I'm pretty sure all my calculations were correct. I also forgot to mention that my answer was not what the answer key said in my other thread. What answer are you getting?

 

[JSGandora]

Someone told me that the equation $\lambda =\lambda_{0}\sqrt{{1-\beta}\over{1+\beta}}$ give the correct answer. Why didn't the usual doppler effect equation work here? I'm confused.