Steps necessary to solve for B

[DumbOne]

Homework Statement

Example 1.9 in the text "Modern Physics for Scientists and Engineers provides an example of Doppler red shift (Where B=v/c)

\sqrt{(1-B)/(1+B)} = 1/3

and provides the answer of B=.08 having solved for B

I am having a problem handling the simple steps necessary to solve for B in the example
Which means I cannot solve the homework problem that involves the Doppler blue shift of an approaching star (see equation below)

Homework Equations

\sqrt{(1-B)/(1+B)}

 

[DumbOne]

As the problem involves blue shift, the Relevant equation is:
\sqrt{(1+B)/(1-B)}

 

[rrogers]

Square, clear the fraction and isolate
1+B=(1/9)(1-B)
B=(-8/9)/(10/9)=-8/10

 

[Mark44]

As the problem involves blue shift, the Relevant equation is:
\sqrt{(1+B)/(1-B)}

That's not an equation.

The equation you gave in your first post was
\sqrt{(1-B)/(1+B)} = 1/3
I'll solve it, but you should be able to apply the same technique to the equation you wind up with for blue shift.

Square both sides of the equation to get
\frac{1-B}{1+B} = 1/9
Multiply both sides by (1 + B):
1 - B = 1/9 * (1 + B)
1 - B = 1/9 + B/9

Add B to both sides, and subtract 1/9 from both sides:
8/9 = 10B/9

Multiply both sides by 9/10:
8/10 = B, or B = .8

This is different from the .08 you reported as the answer.

 

[Mark44]

It probably should be noted that if
\sqrt{(1-B)/(1+B)} = 1/3
then
\sqrt{(1+B)/(1-B)} = 3

The equation that rrogers solved had the revised radical expression on the left, but the same value on the right.

 

[DumbOne]

With your help, the problem was solved.

Thank you both very much.

p.s.
the answer to Example 1.9 was B=0.8
my typo