# Steps necessary to solve for B

• DumbOne
In summary, the conversation discusses an example in the text "Modern Physics for Scientists and Engineers" that involves solving for B in a Doppler red shift equation. The first equation given is \sqrt{(1-B)/(1+B)} = 1/3, and the correct answer is B=0.8. The conversation also addresses a homework problem involving Doppler blue shift, with the relevant equation being \sqrt{(1+B)/(1-B)}. The process for solving the problem is explained, and the correct answer is found to be B=0.8. The conversation concludes with a thank you note and a correction of a previous typo.
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

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

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

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

DumbOne said:
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.

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.

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

## 1. What is the first step in solving for B?

The first step in solving for B is to identify the equation or problem that requires finding the value of B. This will help determine which mathematical operations need to be performed.

## 2. What information do I need to solve for B?

In order to solve for B, you will need at least one known value or variable in the equation. This could be a number, another variable, or a relationship between different values.

## 3. How do I isolate B in an equation?

To isolate B, you will need to use algebraic manipulation to get B on one side of the equation and all other variables and numbers on the other side. This may involve using inverse operations, such as addition and subtraction, multiplication and division, or exponents and roots.

## 4. What if there are multiple variables in the equation?

If there are multiple variables in the equation, you will need to use algebraic techniques, such as substitution or elimination, to eliminate all variables except for B. This will allow you to solve for B using the remaining information in the equation.

## 5. How do I know if my solution for B is correct?

You can check your solution for B by substituting it back into the original equation and solving for both sides. If the values on both sides of the equation are equal, then your solution for B is correct. You can also use a calculator or graphing tool to graph the equation and see if the value of B satisfies the equation.

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