A police car's radar gun emits microwaves with a frequency of f1=7.50 GHz. The beam reflects fro

step 1 When the cars approach, you have F2 to be larger. And the frequency difference, Jelta F equals F

A police car's radar gun emits microwaves with a frequency...

A police car's radar gun emits microwaves with a frequency of $f_{1}=7.50 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving toward the police car at $48.0 \mathrm{m} / \mathrm{s}$ with respect to the police car. The speeder's radar detector detects the microwave at a frequency $f_{2}$. (a) Which is larger, $f_{1}$ or $f_{2} ?$ (b) Find the frequency difference $f_{2}-f_{1}$.

A police car's radar gun emits microwaves with a frequency of $f_{1}=7.50 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving toward the police car at $48.0 \mathrm{m} / \mathrm{s}$ with respect to the police car. The speeder's radar detector detects the microwave at a frequency $f_{2}$.
(a) Which is larger, $f_{1}$ or $f_{2} ?$
(b) Find the frequency difference $f_{2}-f_{1}$.

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Key Concepts

Double Doppler Shift in Reflection

When a moving object reflects an electromagnetic wave, the Doppler shift occurs twice: once when the moving object 'receives' the wave (which is already shifted due to relative motion) and a second time when it reflects the wave back. For non-relativistic speeds, this leads to an approximate frequency difference of twice the shift obtained from a single Doppler effect calculation, making the reflected frequency higher if the object is approaching.

Radar Principle

Radar systems operate by emitting electromagnetic waves that reflect off moving objects. By measuring the frequency shift between the transmitted and received waves, the speed of the moving object can be inferred. This principle is commonly applied in speed detection and tracking technologies.

Doppler Effect

The Doppler effect is the change in frequency of a wave in relation to an observer moving relative to the wave source. In the context of electromagnetic waves, when the source and observer are moving towards one another the observed frequency is higher than the emitted frequency, while if they are moving apart, it is lower.

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