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