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Units And Measurement

Question
CBSEENPH11020567

When a string is divided into three segments of length l1, l2, and l3 the fundamental frequencies of these three segments are v1, v2, and v3 respectively. The original fundamental frequency (v) of the string is

  • square root of straight v space equals space square root of v subscript 1 end root plus square root of v subscript 2 end root plus square root of v subscript 3 end root
  • v = v1 +v2 +v3

  • 1 over straight v space equals space 1 over v subscript 1 space plus 1 over v subscript 2 plus 1 over v subscript 3
  • fraction numerator 1 over denominator square root of straight v end fraction space equals space fraction numerator 1 over denominator square root of v subscript 1 end root end fraction plus fraction numerator 1 over denominator square root of v subscript 2 end root end fraction plus 1 over square root of v subscript 3

Solution

C.

1 over straight v space equals space 1 over v subscript 1 space plus 1 over v subscript 2 plus 1 over v subscript 3

The fundamental frequency of string
straight v equals space fraction numerator 1 over denominator 2 straight l end fraction square root of straight T over straight m end root
straight v subscript 1 straight l subscript 1 space equals straight v subscript 2 straight l subscript 2 space equals space straight v subscript 3 straight l subscript 3 space equals space straight k
From space eq space left parenthesis straight i right parenthesis
straight l subscript 1 space equals space straight k over straight v subscript 1 comma space straight l subscript 2 space equals space straight k over straight v subscript 2 comma straight l subscript 3 space equals space straight k over straight v subscript 3
original space length
straight l equals straight k over straight v
Here comma space straight l equals straight l subscript 1 plus straight l subscript 2 plus straight l subscript 3
straight k over straight v space equals straight k subscript 1 over straight v subscript 1 space plus straight k subscript 2 over straight v subscript 2 plus straight k subscript 3 over straight v subscript 3
1 over straight v space equals 1 over straight v subscript 1 space plus 1 over straight v subscript 2 plus 1 over straight v subscript 3