Electromagnetic Spectrum Problem Help

AI Thread Summary
The problem involves calculating the frequency of an AM radio station based on the height of its antenna, which is 112 meters and represents one-quarter of the wavelength. The correct approach is to multiply the antenna height by four to find the full wavelength, then use the speed of light equation to determine the frequency. The calculated frequency is approximately 6.70 x 10^5 Hz, which falls below the typical AM frequency range of 500 to 1600 kHz. The discussion emphasizes the importance of ensuring the speed of light is used in the correct units. Overall, the solution process is validated, but the frequency suggests a need for further verification against standard AM radio frequencies.
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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