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a closed organ pipe and a open organ pipe of same length L when set into vibrations simultaneously in their fundamental mode produces 2 beats. when their lenghts are changed they produce 7 beats . if new length of organ pipe is Lo and new length of closed organ pipe is Lc then relation between Lc and Lo is ??

a closed organ pipe and a open organ pipe of same length L when set into vibrations simultaneously in their fundamental mode produces 2 beats. when their lenghts are changed they produce 7 beats . if new length of organ pipe is Lo and new length of closed organ pipe is Lc then relation between Lc and Lo is ??

Grade:12

2 Answers

Dewansh
19 Points
5 years ago
For closed organ pipe to vibrate in fundamental mode v/f1 = 4l , For open organ pipe to vibrate in fundamental mode v/f2 = 2l ,on calculating f2 - f1 and equating it to 2 I.e. f2 - f1 = 2 , we get v = 8l . Now , for changed lengths expression becomesClosed organ pipe → v/f`1 = 4 Lc Open organ pipe → v/f`2 = 2 Lo Putting value of v in both , we getClosed organ pipe → Lc = 2l/f`1Open organ pipe →Lo = 4l/f`2
Dewansh
19 Points
5 years ago
On continuation with previous answer f`2 = 4l/Lof`1 = 2l/Lc , this time f`2 - f`1 = 7 ,We get relation 2l/7= (Lc×Lo)/(2Lc-Lo) .

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