Electromagnetic Spectrum Problem Help

In summary, the height of an AM radio station's antenna is 112m and represents one quarter-wavelength of its signal. Using the equation c = f x d, the frequency can be calculated by dividing the speed of light by the product of the height and 4. With this calculation, a frequency of about 6.70 x 10^5 Hz is obtained, which falls within the typical range for AM radio frequencies.
  • #1
TLeo198
8
0

Homework Statement


As you drive by an AM radio station, you notice a sign saying that its antenna is 112m high. If this height represents one quarter-wavelength of its signal, what is the frequency of the station?


Homework Equations


c (speed of light) = f (frequency) x d (wavelength/lambda)


The Attempt at a Solution


It's simply the wording that's messing me up. What I did was multiply 112 meters by 4 since it says that the height represents one-quarter of the wavelength, and simply divided the speed of light by that number to get an answer of about 6.70 x 10^5 Hz. I know radio waves at their smallest are generally 10^6 Hz. Any comments? Any help is greatly appreciated
 
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  • #2
TLeo198 said:

Homework Statement


As you drive by an AM radio station, you notice a sign saying that its antenna is 112m high. If this height represents one quarter-wavelength of its signal, what is the frequency of the station?


Homework Equations


c (speed of light) = f (frequency) x d (wavelength/lambda)


The Attempt at a Solution


It's simply the wording that's messing me up. What I did was multiply 112 meters by 4 since it says that the height represents one-quarter of the wavelength, and simply divided the speed of light by that number to get an answer of about 6.70 x 10^5 Hz. I know radio waves at their smallest are generally 10^6 Hz. Any comments? Any help is greatly appreciated

Check your units and make sure C is in m/s not km/s.
 
  • #3
I made sure that C = 3 x 10^8 m/s, so the answer I obtained came from 3 x 10^8 / (112 x 4) = 6.70 x 10^5 Hz (rounded up to 3 sigfigs). Thanks though.
 
  • #4
Looks good. AM frequencies are about 500 to 1600 kHz, or around 10^6 Hz as you pointed out.
 

1. What is the electromagnetic spectrum?

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. It includes everything from low-frequency radio waves to high-frequency gamma rays.

2. What is an electromagnetic spectrum problem?

An electromagnetic spectrum problem typically involves analyzing and interpreting data related to different types of electromagnetic radiation and their corresponding wavelengths, frequencies, and energies. It may also involve calculating properties such as speed or intensity of electromagnetic waves.

3. What are the applications of understanding the electromagnetic spectrum?

Understanding the electromagnetic spectrum is crucial in many fields, such as astronomy, telecommunications, and medicine. It helps us study and communicate using different types of waves, such as visible light, radio waves, and x-rays. It also allows us to develop technologies like MRI machines and radio telescopes.

4. How can I solve an electromagnetic spectrum problem?

To solve an electromagnetic spectrum problem, you will need to have a good understanding of the properties of electromagnetic waves and how they relate to each other. You will also need to be familiar with the mathematical equations and formulas used to calculate different properties. Practice and applying these concepts to different scenarios will help you become more proficient in solving these problems.

5. What are some common misconceptions about the electromagnetic spectrum?

One common misconception about the electromagnetic spectrum is that all types of radiation are harmful. While some types, such as x-rays and gamma rays, can be harmful in large doses, others, like visible light and radio waves, are harmless to humans. Another misconception is that the electromagnetic spectrum is a linear scale, when in reality, it is a continuous spectrum with overlapping frequencies and energies.

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