modes of vibration in a string
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The two ends are nodes and there is an antinode exactly midway between the two ends. In other words, one complete loop is formed on the string. Since the distance between the two consecutive nodes is λ/2, the length of the string (l).
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The natural modes of a fixed-fixed string
When a string is fixed at both ends, two waves travelling in opposite directions simply bounce back and forth between the ends. The vibrational behavior of the string depends on the frequency (and wavelenth) of the waves reflecting back and forth from the ends.
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