What wavelengths will produce standing waves for a rope with a length of 6.0 m?

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bandmanjoe | Middle School Teacher | (Level 2) Senior Educator

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For a rope of 6 meters, the first standing wave would be the vibration of the entire length, 6 meters.  This represents the lowest wavelength and is called the fundamental, the wavelength upon which all the proceeding wavelengths are based.  The next standing wave occurs when the original length is halved, which would be 3 meters.  The next standing wave occurs when the original length is divided into thirds, so that would be 2 meters, 4 meters, and 6 meters.  The next standing wave that occurs is when the original length is divided into quarters, which would be 1.5 meters, 3 meters, 4.5 meters, and 6 meters.  This gives you the fundamental and the next three standing waves, which in sound, would represent the beginning of an overtone series based on a rope length of 6 meters.

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