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So I was doing Melde's experiment with a vibrator for the source of the wave. With a vibrator instead of a tuning fork, I can adjust the frequency of the vibrator and from here, adjust the frequency of the wave.

Illustration Melde's experiment

Here is an illustrator of the experiment. But instead of connecting it to a pulley, the other end of the string is tight up tightly on a static.

The first thing I was told to do is to change the frequency of the vibrator until I get the wave shape is exactly like a half-phase wave, where the wave nodes are exactly at both ends of the string and the amplitude of the standing wave is approximately at the middle of the wave. From my understanding, the frequency of such a condition is called the fundamental frequency or the first harmonic. Then, I measure the amplitude of the wave with a ruler or meter (which is quite rough).

The next thing to do is to change the frequency until I get the second harmonic frequency and then measure the amplitude. I keep doing this until the fourth harmonic frequency.

Illustration on first and second harmonic.

The thing is, from the result of the experiment, I found that the amplitude decreases as the frequency increases. But, from my understanding too, shouldn't amplitude does not relate with frequency? Shouldn't the amplitude of each harmonic frequency be the same?

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Take a thread, and try to bend it to the shape of first harmonic. Now, keeping the end points unchanged, bend it to the second harmonic. Did the amplitude decrease?

So for higher modes, the wire has to reduce its amplitude for its length to remain the same. Excuse me for the horrible drawing :)

enter image description here

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