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You are playing a violin, where the fundamental frequency of one of the strings is 440...

You are playing a violin, where the fundamental frequency of one of the strings is 440 ??, as you are standing in front of the opening of a long tube that is closed at the other end. As you play, you notice that the first time you hear an echo from the tube is when the sound from the 440 ?? string is in its fourth harmonic. Assuming you are playing this string on earth, what must be the length of the tube? What is the next higher harmonic number for the same string on the violin when you hear the next higher harmonic echo from the tube?

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