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Mechanical Properties Of Fluids

Question
CBSEENPH11020536

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

  • 80 cm

  • 100 cm

  • 120 cm

  • 140 cm

Solution

C.

120 cm

The fundamental frequencies of closed and open organ pipe are given as,
straight v subscript straight o space equals fraction numerator straight v over denominator 4 space l end fraction
straight v subscript straight o space equals space fraction numerator straight v over denominator 2 space straight l apostrophe end fraction
Given the second overtone (i.e. third harmonic) of open pipe is equal to the fundamental frequency of close pipe


i.e 3vo =vo
rightwards double arrow space 3 fraction numerator straight v over denominator 2 straight l apostrophe end fraction space equals space fraction numerator straight v over denominator 4 space straight l end fraction
rightwards double arrow space straight l apostrophe space equals space 6 straight l space equals space 6 space straight x space 20 space equals space 120 space cm