Which of the following lengths will NOT produce standing waves on a rope whose length is 1 m? Choices below:2/3 m 1 m 2 m pi m

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

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If you have a rope whose length is one meter, anything that is longer than the original length would not be a logical answer.  Standing waves are patterns that occur as an overtone series, first as the lowest wavelength possible, which would be the original length of the rope, 1 meter.  This lowest wavelength is also called the fundamental, meaning it is the primary wavelength upon which all the other wavelengths are based.  The next standing wave occurs when you halve the original length, 1 meter, so that would be .5 meters.  This one is not among your choices.  The next one would be where the original length is divided into thirds, 1/3, 2/3, 3/3 (1), which you do have as a choice.  Pi times the original length would be (3.14)(1 m) = 3.14 meters, which exceeds the original length.

So 2/3 meter and 1 meter represent standing overtones, while 2 meters and Pi meters do not.