Cool Question about the doppler effect

In summary: Nope, not really. If the car is going that fast, the light will already be green when it passes the traffic signal. In summary, if you are driving in a car up to a set of traffic lights that are red, you need to be going at a speed of 44 million ms-1 in order to make the lights appear green.
  • #1
benhorris
21
0
If you are driving in a car up to a set of trafic lights that are red, how fast would you need to be going to make the lights appear green? (take the velocity of light to be 3x10^8 ms-1 and the wavelength of red light to be 620nm and the wavelength of green light to be 540nm)

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

Any help greatly apreciated.
 
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  • #2
It helps if you show what you've done so we can see where it went wrong.

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
hehe, yeah i know all that. I am just not sure what the differnce in wavelength is etc. I actually got 38 million metres / sec. Not 44. Just wondering what you got.

:cool:
 
  • #4
okok this is what i did.

620nm - 540nm = 80nm

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

= v

v = 38.6 million ms-1
 
  • #5
Difference in wavelengths? You are given the wavelengths and it's actually the ratio between the wavelengths that is important, not the difference.

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
Sorry, I didn't see your last post.

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
Yep, got it. I had the wrong calculation to begin with.

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?
 

1. How does the doppler effect affect sound?

The doppler effect is a phenomenon where the frequency of a sound wave appears to change when the source of the sound is in motion. As the source moves towards an observer, the frequency of the sound waves increases, resulting in a higher pitch. As the source moves away, the frequency decreases, resulting in a lower pitch.

2. What causes the doppler effect?

The doppler effect is caused by the relative motion between the source of the sound and the observer. It can also occur when the medium through which the sound is passing is in motion, such as when an ambulance passes by and the sound of the siren appears to change pitch.

3. Does the doppler effect only apply to sound waves?

No, the doppler effect can also be observed in other types of waves, such as light waves. This is known as the doppler shift, where the frequency of light appears to change depending on the relative motion between the source of light and the observer.

4. How is the doppler effect used in real life?

The doppler effect has many practical applications, such as in radar and sonar systems. It is also used in medical imaging techniques, such as ultrasound, to determine the direction and speed of blood flow in the body.

5. Can the doppler effect be observed in space?

Yes, the doppler effect can also be observed in space. For example, the redshift of light from distant galaxies is due to the doppler effect, as the galaxies are moving away from Earth and their light waves appear to have a longer wavelength.

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