Electromagnetic Spectrum Problem Help

[TLeo198]

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

 

[LowlyPion]

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.

 

[TLeo198]

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.

 

[Redbelly98]

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