Suppose that a police car on the highway is moving to the right at 27 m/s, while a speeder is coming up from almost directly behind at a speed of 35 m/s, both speeds being with respect to the ground. The police officer aims a radar gun at the speeder. Assume that the electromagnetic wave emitted by the radar gun has a frequency of 7.00 109 Hz. Find the the difference between the frequency of the wave that returns to the police car after reflecting from the speeder's car, and the original frequency emitted by the police car.

1 Hz
The wave that returns to the police car has the greater frequency.
The emitted wave has the greater frequency.

To find the difference in frequency between the wave that returns to the police car after reflecting from the speeder's car and the original frequency emitted by the police car, we can use the concept of the Doppler effect.

The Doppler effect describes the change in frequency of a wave as perceived by an observer moving relative to the source of the wave.

In this case, the observer is the police car, moving to the right at 27 m/s, and the source of the wave is the speeder's car.

The formula for the Doppler effect is given by:

Δf/f = v/c

Where:
Δf is the change in frequency
f is the original frequency emitted by the source (7.00 x 10^9 Hz)
v is the relative velocity between the observer and the source (27 m/s - (-35 m/s) = 62 m/s)
c is the speed of light (approximately 3.00 x 10^8 m/s)

Plugging in the values:

Δf/ (7.00 x 10^9 Hz) = (62 m/s) / (3.00 x 10^8 m/s)

Δf = (7.00 x 10^9 Hz) * (62 m/s) / (3.00 x 10^8 m/s)

Δf = 1.44 x 10^5 Hz

Therefore, the difference between the frequency of the wave that returns to the police car after reflecting from the speeder's car and the original frequency emitted by the police car is 1.44 x 10^5 Hz.

To find the difference between the frequency of the wave that returns to the police car after reflecting from the speeder's car and the original frequency emitted by the police car, we need to consider the Doppler effect.

The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.

In this scenario, the police car is moving towards the speeder's car, so the observer (police officer) is moving towards the source of the wave (speeder's car). This is known as a positive Doppler effect because the observer is approaching the source.

The formula for the Doppler effect in this case is given by:

f' = (c + v₁) / (c - v₂) * f,

where f' is the frequency observed by the police officer, c is the speed of light (approximately 3.00 x 10^8 m/s), v₁ is the velocity of the police car (27 m/s to the right), v₂ is the velocity of the speeder's car (35 m/s), and f is the original frequency emitted by the police car (7.00 x 10^9 Hz).

Plugging in the given values, we can calculate the difference in frequency:

f' = (3.00 x 10^8 + 27) / (3.00 x 10^8 - 35) * 7.00 x 10^9 Hz

f' ≈ 7.009 Hz

Therefore, the difference between the frequency of the wave that returns to the police car after reflecting from the speeder's car and the original frequency emitted by the police car is approximately 7.009 Hz.