Doppler effect: finding recession speed from wavelength shift

[Pushoam]

Homework Statement

Homework Equations

The Attempt at a Solution

When the source is not moving, $\lambda = 6250 A$ ...(1)

When the source is moving, $\lambda ' = 6500 A$ ...(2)

From (1) and (2),

$\lambda ' > \lambda$ ...(3)

This means that the source is moving away from the Earth.

$\nu ' = \nu \sqrt{ \frac { c+v}{c-v}$

${\frac { \lambda }{\lambda '} }^2 = { \frac { c+v}{c-v}$

0.9245c –c = v(1+0.9245)

V =11760 km/s

Is this correct?

 

[Orodruin]

0.9245c –c = v(1+0.9245)

I hope you meant to write c - 0.9245c in the left-hand side. Otherwise the argumentation and the result seem fine.

 

[Pushoam]

I hope you meant to write c - 0.9245c in the left-hand side.

I meant to write the following:

0.9245c –c = v(1+0.9245)

The following is wrong:

V =11760 km/s

The speed v is negative implying that the star is moving away from the Earth.
v = - 11760 km/s

 

[Pushoam]

$\nu ' = \nu \sqrt{ \frac { c+v}{c-v}$
${\frac { \lambda }{\lambda '} }^2 = { \frac { c+v}{c-v}$

$\nu ' = \nu \sqrt{ \frac { c+v}{c-v}}$
${\frac { \lambda }{\lambda '} }^2 = { \frac { c+v}{c-v} }$

 

[Orodruin]

Speed can never be negative as it is the absolute value of velocity. Whether the velocity is negative or not depends on which direction you defined as positive.

 

[Pushoam]

Speed can never be negative as it is the absolute value of velocity. Whether the velocity is negative or not depends on which direction you defined as positive.

I had the impression that speed is a scalar quantity, which can be either positive or negative.
Now, I got to know that speed is defined as magnitude of velocity.

Then $\vec v = v \hat v$ where $\hat v$ is a positive constant unit vector and v could be either positive or negative and it has no specific name.
So, the following is wrong.

The speed v is negative implying that the star is moving away from the Earth.

The correct one is :
v is negative implying that the star is moving away from the Earth.
v = - 11760 km/s

 

[Orodruin]

If you defined the positive direction to be moving towards the star, yes. Rounding the speed gives you one of the available answers.