- #1

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Ive calculated it wrong... :s and found it to be 44 million ms-1.

Any help greatly apreciated.

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- Thread starter benhorris
- Start date

- #1

- 21

- 0

Ive calculated it wrong... :s and found it to be 44 million ms-1.

Any help greatly apreciated.

- #2

Galileo

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The approach to the problem is simple: Take the formula for the doppler shift:

[tex]\frac{\lambda '}{\lambda}=\sqrt{\frac{c-v}{c+v}}[/tex]

where [itex]\lambda '[/itex] is the Doppler-shifted wavelength and [itex]v[/itex] is the relative velocity between source and observer (positive when approaching).

The unknown is v, so solve your equation for v and just plug in the numbers.

- #3

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- #4

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okok this is what i did.

620nm - 540nm = 80nm

(80nm / 640nm) * 3x10^8

= v

v = 38.6 million ms-1

620nm - 540nm = 80nm

(80nm / 640nm) * 3x10^8

= v

v = 38.6 million ms-1

- #5

Galileo

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The answer is higher that 38 Mm/s and lower than 44 Mm/s (Mm= Megameter :) ) so you probably did something wrong. What's your expression for v?

- #6

Galileo

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Well, I`m not sure what your reasoning is. I don't why you took the difference in wavelengths and not just solve the expression for the doppler shift for v in terms of lamda and lambda'.

The answer comes quite close to the actual answer, because when the v<<c the approximation:

[tex]\frac{\lambda'}{\lambda}=1-v/c[/tex]

can be used. This is easily solvable for v:

[tex]v=c(1-\frac{\lambda'}{\lambda})=c\frac{\lambda-\lambda'}{\lambda}[/tex]

which becomes exactly your calculation.

- #7

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But now you know what you have to do to beat the red lights. Travel 38 million metres per second, then the red light will magically turn green. Perfect hey?

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