Doppler and electromagnetic waves

In summary, The speeder's speed with respect to the ground can be calculated using the formula vrel = (fo - fs)c/fo, where fo is the emitted frequency of the radar gun, fs is the measured frequency of the reflected wave, and c is the speed of light. In this scenario, the speeder's speed was found to be 4.98 x 10^2 m/s.
  • #1
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A speeder is pulling directly away and increasing his distance from a police car that is moving at 23 m/s with respect to the ground. The radar gun in the police car emits an electromagnetic wave with a frequency of 6.0 109 Hz. The wave reflects from the speeder's car and returns to the police car, where its frequency is measured to be 316 Hz less than the emitted frequency. Find the speeder's speed with respect to the ground.

fo = fs * (1 +- vrel/c)

I am stressing out and can't get this at all
 
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  • #2
.Answer: The speed of the speeder with respect to the ground is vrel = (fo - fs)c/fo = (6.0x109-316x106)c/6.0x109 = 4.98 x 10^2 m/s
 
  • #3


I can understand your frustration with this problem. Let's break it down step by step to better understand what is happening.

First, we need to understand the concept of the Doppler effect. This is the change in frequency of a wave (in this case, the electromagnetic wave emitted by the radar gun) due to the relative motion between the source of the wave (the radar gun) and the observer (the police car). When the source and observer are moving towards each other, the frequency of the wave appears to increase. When they are moving away from each other, the frequency appears to decrease.

In this scenario, the speeder's car is moving away from the police car, so we know that the reflected wave will have a lower frequency than the emitted wave. The formula you provided, fo = fs * (1 +- vrel/c), is the equation for the Doppler effect, where fo is the observed frequency, fs is the emitted frequency, vrel is the relative velocity between the source and observer, and c is the speed of light.

We are given that the emitted frequency is 6.0 * 10^9 Hz and the observed frequency is 316 Hz less than that. Plugging these values into the formula, we get:

6.0 * 10^9 Hz = fs * (1 - vrel/c)

(1 - vrel/c) = (6.0 * 10^9 Hz) / (fs)

We don't know the value of fs, but we can solve for it by using the fact that the police car is moving at 23 m/s with respect to the ground. We can use the formula for velocity, v = d/t, where v is velocity, d is distance, and t is time. In this case, the distance between the police car and the speeder's car is increasing, so we can use the formula d = v * t, where d is the change in distance, v is the velocity, and t is the change in time.

We know that the change in distance is equal to the change in frequency, so we can set these two equations equal to each other:

(1 - vrel/c) = (6.0 * 10^9 Hz) / (fs)

d = v * t

We can rearrange the first equation to solve for fs:

fs = (6.0 * 10^9 Hz) / (1
 

1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave. This effect is commonly experienced with sound waves, where the frequency of a sound appears to change as the source moves closer or farther away from the listener.

2. How does the Doppler effect apply to electromagnetic waves?

The Doppler effect also applies to electromagnetic waves, such as light or radio waves. In this case, the frequency and wavelength of the wave appear to change as the source or observer moves relative to each other. For example, the color of a star may appear to shift towards the blue end of the spectrum if it is moving towards us, and towards the red end if it is moving away from us.

3. What is the difference between a transverse and longitudinal wave?

A transverse wave is a wave in which the particles of the medium vibrate perpendicular to the direction of wave propagation. A good example of this is a water wave. On the other hand, a longitudinal wave is a wave in which the particles of the medium vibrate parallel to the direction of wave propagation. Sound waves are an example of longitudinal waves.

4. How is the speed of an electromagnetic wave determined?

The speed of an electromagnetic wave is determined by the medium in which it is traveling. In a vacuum, electromagnetic waves travel at the speed of light, which is approximately 299,792,458 meters per second. In different materials, such as air or water, the speed of electromagnetic waves may vary.

5. Can electromagnetic waves be harmful?

Electromagnetic waves can be harmful at certain frequencies and intensities. For example, ultraviolet (UV) radiation from the sun can cause damage to our skin and eyes. X-rays and gamma rays, which have higher frequencies and shorter wavelengths, can be harmful to our bodies if we are exposed to them in large amounts. However, most electromagnetic waves, such as visible light and radio waves, are not harmful to humans.

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