Imagine a ruler that you lay over the edge of a table. The longer it sticks out, the deeper the sound it makes when made vibrate. The more it sticks out, the further it needs to travel in one swing to reach the point where the material stretches so much that it makes it travel back. Therefore the frequency with which it oscillates (how many rounds per time unit does it swing back and forth) is lower. Lower frequency equals lower pitch.
With the xylophpne its similar, only that it rests on two eges and the distance between the define how much material has to move.
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