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The vibration of a string held at both ends can be seen at a superposition of vibration patterns called 'modes'. Each mode contains its own shape and frequency. When the string is plucked, it will vibrate as a superposition of these modes. Therefore, the sound it creates can be heard as a combination of different frequencies, called harmonics.
In this animation, we see a string vibrating from a superposition of modes. You can change the modes of vibrations by adjusting the checkboxes and clicking 'Apply'. Notice how each mode contains a different shape but also vibrates at different frequencies.