Now take a line of LEDs, and set them up so that they each blink in turn, again at some high frequency, so that what you have is a moving point of light that runs down the line faster than you can see it. If you pluck the string in front of this line you will see each point of the string as it rides up and down on it's own stack of sine waves, frozen at a different part of the cycle. If you pluck the string in the center the resulting humps will be rounded, but as you move toward the end the humps will get squarer as more high harmonics are introduced. As long as the blink rate is right you will see the proper number of humps on any part of the string. Your TV or computer monitor is a sort of strobe device that redraws the picture a number of times every second.
Computer monitors have more lines than TVs, so they are even faster.
Thus, your computer monitor is a combination of the two kinds of blinking lights discussed above, having crosswise adjacent lines that blink in succession down the screen, and the TV is much the same. When you hold your harp so that the strings run up and down the screen you will see a number of humps, depending on how many cycles the string makes each time the screen is refreshed, just as you did with the lights that blink in succession along the length of the string. It is harder to see anything that makes any sense when you hold the string so that it runs across the screen. I think this would make a great science fair project. You could look at things like inharmonicity and the exact 'recipe' of harmonics in a string fairly easily this way.