How Do Sinusoids Combine to Create Complex Waveforms?

In summary: Two waves of the same amplitude but a small difference in frequency will produce a waveform with a period that is the sum of the two periods.
  • #1
clphipps
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0
I am taking a circuits class. The professor has given us a waveform. I was trying to figure out what it takes to create the waveform. The professor give us a hint that it was a combination of sinusoids. I am at a loss.

The wave appears to have a DC offset of -2. The wave appears to have fluctuating amplitudes. The amplitude starts off small and increases until in reaches an amplitude of 10 Once the amplitude reaches 10 it decreases back to the original amplitude. Once the amplitude decreases until it reaches the smallest amplitude it increases again. So the wave is symmetric it 2 ways. It is symmetric around the amplitudes as well as symmetric around the DC offset.

I am at a loss. I would like to figure out what creates the waveform, and then I must use the waveform in a PSpice simulation.

Is there a way to upload an image?

Any help would greatly be appreciated.

Thank you
 
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  • #2
Welcome to PF,

Use the attachment button (it has a paperclip icon) that is present above the reply box. It will take a while for the attachment to be approved. Alternatively, you could use any number of websites that allow users to upload images.
 
  • #3
Ok let's try this.

This is a picture of the sine wave that needs to be identified. Any help would greatly be appreciated. Thank you.
 

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  • #4
This looks to me like the product of two sine waves. One of these waves forms an envelope that the other one oscillates in.

The wave form that is the envelope has a period of 10 sec. and an amplitude of 10 V, and is shifted down by 2 V. I would guess that the other wave form has an amplitude of 1 V. If you count the number of oscillations you should be able to get the period.
 
  • #5
What happens when you superimpose two sine waves of the same amplitude, but a small difference in frequency, between them? (hint: beat)
 
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FAQ: How Do Sinusoids Combine to Create Complex Waveforms?

What is a combination of sinusoids?

A combination of sinusoids refers to a function that can be expressed as the sum of two or more sinusoidal functions with different frequencies, amplitudes, and phases. It is often used to describe complex waveforms that are composed of simpler sinusoidal components.

How do you graph a combination of sinusoids?

To graph a combination of sinusoids, you need to plot each individual sinusoidal function on the same coordinate system, taking into account their respective frequencies, amplitudes, and phases. The resulting graph will show the combined waveform, which may exhibit characteristics such as beats, interference patterns, or resonances.

What are some real-world applications of combinations of sinusoids?

Combinations of sinusoids are commonly used in fields such as physics, engineering, and signal processing. Some examples include modeling sound waves, analyzing electrical signals, and designing filters for signal processing. They are also used in music and acoustics to create complex and interesting sounds.

How do you find the frequency, amplitude, and phase of a combination of sinusoids?

To determine the frequency, amplitude, and phase of a combination of sinusoids, you can use techniques such as Fourier analysis or spectral decomposition. These methods involve breaking down the combined waveform into its individual sinusoidal components and analyzing their properties.

What is the difference between a combination of sinusoids and a single sinusoidal function?

A combination of sinusoids is a function that is composed of two or more sinusoidal components, while a single sinusoidal function is a basic sinusoidal wave with a specific frequency, amplitude, and phase. Combinations of sinusoids can exhibit more complex behavior and can be used to model a wider range of phenomena compared to single sinusoidal functions.

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