Q.

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

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a

120 cm

b

140 cm

c

80 cm

d

100 cm

answer is A.

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Detailed Solution

For closed organ pipe, fundamental frequency is given byvc=v4l For open organ pipe, fundamental frequency is given by vo=v2l'2nd  overtone of open organ pipe v'=3vo;v'=3v2l' According to question, vc=v'v4l=3v2l'l'=6l Here, l=20 cm,l'=?∴  l'=6×20=120 cm
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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