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Physical Chemistry (Doppler-shifted wavelength)

I'm trying to solve a question but I'm unsure if I'm attempting it correctly.

What is the Doppler-shifted wavelength of a red (680 nm) traffic light approached at 60 km/h?

I'm using the Doppler shift equation:

Attachment not found


I've converted s (speed) into m/s and wavelength into m so they are consistent with the units for c (speed of light). The answer in the back of the book is 0.9999 (times the wavelength) but I can't quite figure out how to get that answer...

(Sorry, first post here; a little unsure how this works...)
(edited 7 years ago)
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What speed did you get?
Reply 2
Avatar for mgawd.no
mgawd.no
OP
Original post by KombatWombat
What speed did you get?


Thanks for replying!

Ok, so I used these variables:

s = 16.67 m/s
c = 3 x 108 m/s
and approaching λ = 680 x 10-9 m.

After plugging them into the Doppler shift equation, I got:

680 x 10-9 = (1.000000056)λ

Solving for λ:

6.799999619 x 10-7 m

I assumed that, because it asked to find the shift, I needed to subtract the two wavelengths which gave me:
3.81 x 10-14 but this is nowhere near the answer.
Lambda approach is your new shifted wavelength so your answer should be 1/(1.000000056)λ
And if you read they question carefully, it's not asking for the shift in the wavelength but the shifted wavelength - no need to find the difference!
Reply 4
Avatar for mgawd.no
mgawd.no
OP
Original post by KombatWombat
Lambda approach is your new shifted wavelength so your answer should be 1/(1.000000056)λ
And if you read they question carefully, it's not asking for the shift in the wavelength but the shifted wavelength - no need to find the difference!


Hm, why did you you take 1/(1.000000056)? I mean, it gives the correct answer but... If I'm solving for 'lambda approach', then shouldn't the answer simply be (1.000000056)λ?

Because, according to the Doppler shift equation:

λ approach. = (1.000000056) λ

Thanks again.

EDIT:

I'm assuming that the Doppler shift expression was simplified to 1/(1.000000056) λ because s<<c.

Am I right?
(edited 7 years ago)
Original post by mgawd.no
Hm, why did you you take 1/(1.000000056)? I mean, it gives the correct answer but... If I'm solving for 'lambda approach', then shouldn't the answer simply be (1.000000056)λ?

Because, according to the Doppler shift equation:

λ approach. = (1.000000056) λ

Thanks again.

EDIT:

I'm assuming that the Doppler shift expression was simplified to 1/(1.000000056) λ because s<<c.

Am I right?

Sorry, I replied to you just before an inorganic exam, not the best time to be thinking of this sort of thing!

Your formula is for frequency, that's why you're getting the reciprocal of the right answer.

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