Electromagnetic Spectrum Problem Help

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Homework Help Overview

The problem involves calculating the frequency of an AM radio station based on the height of its antenna, which is given as 112 meters, representing one quarter of the wavelength of the signal. The context is within the electromagnetic spectrum, specifically focusing on radio waves.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the antenna height and wavelength, with one participant attempting to calculate the frequency by multiplying the height by four and then using the speed of light. There is also a focus on ensuring the correct units are used in the calculations.

Discussion Status

Some participants have confirmed their calculations and discussed the expected frequency range for AM radio stations. There is an acknowledgment of the importance of unit consistency in the calculations, and while one participant expresses uncertainty about the wording, another confirms their approach.

Contextual Notes

Participants are working under the constraints of the problem statement and are checking assumptions related to the relationship between wavelength and frequency as well as the units of measurement used.

TLeo198
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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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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.
 
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.
 
Looks good. AM frequencies are about 500 to 1600 kHz, or around 10^6 Hz as you pointed out.
 

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