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 ??

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

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) .