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Waves

Question
CBSEENPH11020834
Wired Faculty App

The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?

  • 10 Hz

  • 20 Hz

  • 30 Hz

  • 40 Hz

Solution

B.

20 Hz

Two successive frequencies of closed pipe
fraction numerator nv over denominator 4 straight l end fraction space equals space 220 space.... left parenthesis straight i right parenthesis fraction numerator left parenthesis straight n plus 2 right parenthesis straight v over denominator 4 straight l end fraction space space equals space 260 space.... space left parenthesis ii right parenthesis Dividing space left parenthesis ii right parenthesis space by space left parenthesis straight i right parenthesis comma space we space get fraction numerator straight n plus 2 over denominator straight n end fraction space equals space 260 over 220 equals 13 over 11 11 straight n space plus space 33 space equals space 13 straight n straight n space equals space 11 so comma space 11 fraction numerator straight v over denominator 4 straight l end fraction space equals space 220 fraction numerator straight v over denominator 4 straight l end fraction space equals space 20

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