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Steps necessary to solve for B

  1. Jan 31, 2009 #1
    1. The problem statement, all variables and given/known data

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

    [tex]\sqrt{(1-B)/(1+B)}[/tex] = 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)
    2. Relevant equations



    [tex]\sqrt{(1-B)/(1+B)}[/tex]
     
  2. jcsd
  3. Jan 31, 2009 #2
    As the problem involves blue shift, the Relevant equation is:
    [tex]\sqrt{(1+B)/(1-B)}[/tex]
     
  4. Jan 31, 2009 #3
    Square, clear the fraction and isolate
    1+B=(1/9)(1-B)
    B=(-8/9)/(10/9)=-8/10
     
  5. Jan 31, 2009 #4

    Mark44

    Staff: Mentor

    That's not an equation.

    The equation you gave in your first post was
    [tex]\sqrt{(1-B)/(1+B)} = 1/3[/tex]
    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
    [tex]\frac{1-B}{1+B} = 1/9[/tex]
    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.
     
  6. Jan 31, 2009 #5

    Mark44

    Staff: Mentor

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

    The equation that rrogers solved had the revised radical expression on the left, but the same value on the right.
     
  7. Jan 31, 2009 #6
    With your help, the problem was solved.

    Thank you both very much.

    p.s.
    the answer to Example 1.9 was [tex]B[/tex]=0.8
    my typo
     
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