Question

How fast would a motorist have to be traveling for a yellow (1 = 590 nm) traffic light to appear green (1 = 550 nm) because of the Doppler shift?

Answer 1

To calculate the motorist's speed to see a yellow light as green due to the Doppler effect, use the Doppler shift equation for light, find the change in wavelength, and then solve for the speed.

Step-by-step explanation:

The question is asking about the Doppler shift of light, which occurs when there is relative motion between a source of light and an observer. In this case, a motorist is moving towards a yellow traffic light (with wavelength λ = 590 nm) fast enough for the light to appear green (with wavelength λ = 550 nm). To find the required speed, we use the Doppler shift equation for light:

Δλ / λ = v / c

Where Δλ is the change in wavelength, λ is the original wavelength, v is the velocity of the observer (motorist), and c is the speed of light (approximately 3.0 × 10⁸ m/s).

To calculate the speed:

1. First, calculate the change in wavelength: Δλ = 590 nm - 550 nm = 40 nm.
2. Convert the wavelength change to meters: 40 nm × (1 x 10⁹ m/nm).
3. Substitute the values into the Doppler shift equation and solve for v.

Using these steps, we can find the motorist's required speed to make the yellow light appear green due to the Doppler effect.