# Homework Help: AM radio signal superimpostion/modulation

1. Aug 15, 2011

### sillyquark

1. The problem statement, all variables and given/known data

Describe how the concept of wave superimposition is used to create AM radio waves.

2. Relevant equations

3. The attempt at a solution

O.K, I am not sure that I understand how this works. In the picture attached it shows the carrier frequency inside of the audio signal. The amplitude changes over time, so is the amplitude not proportional to the wavelength or frequency? If that is the case then would I be correct in saying that constructive/destructive wave interference is used to superimpose the amplitude of the carrier frequency to be similar with the audio signal's wavelength. Wave demodulation for AM signals measures the amplitude over time so that the wavelength can be known. With the wavelength and speed of light one can calculate the frequency of the audio signal, which is then amplified and converted into sound through the speakers.

Is this more or less correct?

#### Attached Files:

• ###### AM superimposition.png
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2. Aug 15, 2011

### Delphi51

Change the last word to "amplitude". AM is amplitude modulation, not frequency modulation. There is, of course a broadening of the frequency range from virtually a single carrier frequency to the range carrier - audioFreq to carrier + audioFreq, but you have not been asked about that.

3. Aug 15, 2011

### sillyquark

So, superimposing the amplitude of the carrier frequency to be similar with the audio signal's amplitude/time gives us wavelength or frequency?

4. Aug 15, 2011

### genxium

Dear sillyquark, AM wave is generated by modulating the carrier wave's amplitude proportional to the signal wave's instantaneous y offset from the x axis (Suppose that you draw a standard Y-X coordinate to plot the signal wave), your attachment plot is an AM wave, with Both Side-Band

5. Aug 15, 2011

### sillyquark

You didn't really answer my question, you just stated what the attachment displays.

6. Aug 15, 2011

### genxium

Sorry about that, I didn't get your idea just now.

I guess you're asking about this $$Y_{am}(t)=(A_c+A_s \cdot cos(2 \pi f_s t)) \cdot cos(2 \pi f_c t)$$ ?

I'm not familiar with Latex in this forum, it took me so much time to adapt to it....

7. Aug 15, 2011

### Delphi51

It doesn't "give us wavelength or frequency". It gives the complex waveform at the bottom of your attachment picture. It has the carrier frequency waveform modulated in amplitude according to the audio signal.

8. Aug 16, 2011

### sillyquark

O.K, I understand the concept but not thoroughly. Thanks for the help, this is all I should need for the answer. Genxium, what are the variables in the equation you posted?

9. Aug 16, 2011

### genxium

A : Amplitude , f: frequency , c: carrier , s: signal.

and this is the simpliest example while the signal wave is a sinusoid wave, but according to Fourier's Theorem, any real wave could be regarded as a superposition of many sinusoid waves, this basic form is still useful in analysis

10. Aug 16, 2011

### sillyquark

Great, thanks, you've helped a lot.

11. Aug 16, 2011

### George Jones

Staff Emeritus
And, in this case, a standard simple identity involving $\cos A \cos B$ gives the superposition.