Writing down algebraic expression

In summary: You're welcome!In summary, the question is asking for the algebraic expression for the fractional change in wavelength between the observed and emitted light from an object moving away from the observer at a small relative speed compared to the speed of light. This can be calculated using the classical Doppler shift formula, which simplifies to -C/v in this scenario.
  • #1
thundercats
11
0

Homework Statement


An object emitting light with a wavelength of L is traveling away from you with a relative speed of v, which is small compared to the speed of light. Write down the algebraic expression for the fractional change in wavelength between what you observe and what the object emits. (In other words, you're trying to find Delta L/L



Homework Equations


F'=F(1-(U/C)) minus sign because its moving away
F=C/L L= lambda :D


The Attempt at a Solution


i just can't seem to be able to rearrange the equation to a point i have
change in wavelenght/wave lenght
i mean i know L of source/L observed= 1- U/C where u is relative speed while c is the speed of light i can't seem to get any further. i would appreciate it if someone is able to show me how to rearrange this equation
 
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  • #2
HINT:

[tex]f^\prime = f\left(1-\frac{u}{c}\right)[/tex]

[tex]\begin{align*}\Rightarrow f^\prime - f & = f\left(1-\frac{u}{c}\right) - f = f\left(1-\frac{u}{c}-1\right)\\
& = - f\frac{u}{c}\end{align*}[/tex]
 
  • #3
so does that mean that delta L/L= C/v. and since v is smaller than the speed of light would the answer be delta L (L is lambda)/L=C
 
  • #4
thundercats said:
so does that mean that delta L/L= C/v.
That would be correct.
thundercats said:
and since v is smaller than the speed of light would the answer be delta L (L is lambda)/L=C
No. I think that what the question meant was that we could use the classical Doppler shift (as we did) rather than the relativistic one.

Note that if v << C then (C/v) >> C.
 
  • #5
thnx by the way
 

Related to Writing down algebraic expression

1. What is an algebraic expression?

An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It does not have an equal sign and cannot be solved as it is.

2. How do I write down an algebraic expression?

To write down an algebraic expression, you need to identify the variables and constants in the given problem. Then, use mathematical operations to combine them in the required order. Remember to use parentheses to indicate the order of operations.

3. What are the basic rules for writing down algebraic expressions?

The basic rules for writing down algebraic expressions are:

  • Use letters to represent variables.
  • Use numbers to represent constants.
  • Use mathematical operators, such as +, -, *, and /, to combine the variables and constants.
  • Use parentheses to indicate the order of operations.

4. Can I use words in an algebraic expression?

No, algebraic expressions only use letters, numbers, and mathematical operators. Words should be translated into symbols in order to write an algebraic expression.

5. How do I simplify an algebraic expression?

To simplify an algebraic expression, you need to combine like terms. Like terms have the same variables with the same exponents. Then, use the distributive property and combine any remaining like terms. Finally, perform any necessary operations to get a final simplified expression.

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