ac - What exactly are harmonics and how do they "appear"? - Electrical Engineering Stack Exchange
If the fundamental frequency were Hz, the harmonics would be Hz, (Listen to the difference between 'pure' and equal temperament at this site, of all because they have an increasingly lower amplitude than the fundamental. What is the relationship between harmonics and wave amplitude in a resonant object? Lets say we have an object which has a natural. Then there's the third harmonic (square waves don't have even harmonics), the purple one. Its amplitude is 1/3 of the fundamental, and you can.
Unless you start thinking about rates of change, I don't think you can answer this question properly. To understand why, imagine a large spring with a very heavy weight which is attached to a handle via fairly loose spring. Pulling on the handle will not directly move the heavy weight very much, but the large spring and weight will have a certain resonant frequency, and if one moves the handle back and forth at that frequency, one can add energy to the large weight and spring, increasing the amplitude of oscillation until it's much larger than could be produced "directly" by pulling on the loose spring.
The most efficient way to transfer energy into the large spring is to pull in a smooth pattern corresponding to a sine wave--the same movement pattern as the large spring. Other movement patterns will work, however. If one moves the handle in other patterns, some of the energy that gets put into the spring-weight assembly during parts of the cycle will be taken out during others. As a simple example, suppose one simply jams the handle to the extreme ends of travel at a rate corresponding to the resonant frequency equivalent to a square wave.
Moving the handle from one end to the other just as the weight reaches end of travel will require a lot more work than would waiting for the weight to move back some first, but if one doesn't move the handle at that moment, the spring on the handle will be fighting the weight's attempt to return to center.
Nonetheless, clearly moving the handle from one extreme position to the other would nonetheless work. Describe what happens to each of the different present functions if you decrease the number of harmonics. Use the simulation to make a Sum Graph that looks like the graph below using only 2 harmonics.
Draw what you think the Sum Graph will look like for the harmonics displayed below. Use the simulation to test your prediction and make corrections with a different color pen.
Waves and Harmonics
Record the amplitudes that you used and write a plan for how you could predict the sum of waves. Use your predictions ideas to draw the sum of these waves.
Test your ideas using the simulation. Make corrections on the predicted graph with a different color pen. Correct your plans for prediction also. Design a test for your ideas on wave addition.
Explain in detail your experiment and the results. Include evidence that your prediction method is repeatable. Wave Game Lowest Score Wins! Use the Level 1 for the beginning of the competition. Press New Game, think about what should work, and then type in your guess in the Amplitude box.
In Level 2, you have to choose one of two harmonics.
Harmonic - Wikipedia
Press New Game, decide which harmonic to use, think about what should work, and then type in their guess in the Amplitude box. In Level 3, you have to choose one of eleven harmonics. In the other Levels, you have to choose more than one wave to add to make the SUM. Start the stopwatch as the player presses the New Game button. The seconds that it takes to match divided by the level number is the score.
This example shows that harmonics can extend to frequencies greater than 0.
You don't notice them in b because their amplitudes are too low. Figure c shows the frequency spectrum plotted on a logarithmic scale to reveal these low amplitude aliased peaks.
At first glance, this spectrum looks like random noise. It isn't; this is a result of the many harmonics overlapping as they are aliased. It is important to understand that this example involves distorting a signal after it has been digitally represented. If this distortion occurred in an analog signal, you would remove the offending harmonics with an antialias filter before digitization.
Harmonic aliasing is only a problem when nonlinear operations are performed directly on a discrete signal. Even then, the amplitude of these aliased harmonics is often low enough that they can be ignored. The concept of harmonics is also useful for another reason: You can view the frequencies between these samples as 1 having a value of zero, or 2 not existing.
Either way they don't contribute to the synthesis of the time domain signal. In other words, a discrete frequency spectrum consists of harmonics, rather than a continuous range of frequencies.
This requires the time domain to be periodic with a frequency equal to the lowest sinusoid in the frequency domain, i.