Question

A physicist drives through a stop light. When he is pulled over, he tells the police officer that the Doppler shift made the red light of wavelength 650nm appear green to him, with a wavelength of 520nm . The police officer writes out a traffic citation for speeding. How fast was the physicist traveling, according to his own testimony?

Answer 1

The physicist traveling, according to his own testimony at -6.6 × 10⁷ m/s.

How fast was the physicist traveling, according to his own testimony?

Using the formula for doppler shift for light,

λ' = λ√[(1 + v/c)/(1 - v/c)] where

• λ = wavelength of source,
• λ' = wavelength of observer,
• v = speed of source and
• c = speed of light

Given that the driver is moving away from the stop light, we take the driver as the source. Since, the Doppler shift made the red light of wavelength 650nm appear green to him, with a wavelength of 520nm. we have

• λ' = wavelength of source = 650 nm,
• λ' = wavelength of observer = 520 nm

So, substituting the values of the variables into the equation, we have

λ' = λ√[(1 + v/c)/(1 - v/c)]

520 nm = 650 nm√[(1 + v/c)/(1 - v/c)]

520/650 = √[(1 + v/c)/(1 - v/c)]

0.8 = √[(1 + v/c)/(1 - v/c)]

Squaring both sides, we have

0.8² = (1 + v/c)/(1 - v/c)

0.64 = (1 + v/c)/(1 - v/c)

0.64(1 - v/c) = (1 + v/c)

0.64 - 0.64v/c = 1 + v/c

0.64 - 1 = v/c + 0.64v/c

-0.36 = 1.64v/c

-0.2195 = v/c

v = -0.22c

v = -0.22 × 3 × 10⁸ m/s

v = -0.66 × 10⁸ m/s

v = -6.6 × 10⁷ m/s

So, the physicist traveling, according to his own testimony at -6.6 × 10⁷ m/s.

Learn more about doppler shift for light here:

brainly.com/question/28499579

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