The length of wire between the two ends of a sonometer is 105 cm. Where should the two bridges be placed so trhat the fundamental frequencies of the three segments are in the ratio of 1:3:15 ?

The length of wire between the two ends of a sonometer is 105 cm. Wher

1.	The length of wire between the two ends of a sonometer is 105 cm. Where should the two bridges be placed so trhat the fundamental frequencies of the three segments are in the ratio of 1:3:15 ?
Answer» SOLUTION :Total length of the WIRE, `L=105 CM` `v_(1):v_(2):v_(3)=1:3:15` Let `L_(1),L_(2) and L_(3)=1:1/3:1/15=15:5:1` Sum of the RATIOS `=15+5+1=21` `therefore L_(1)=15/21105==75CM, L_(2)=5/21105=25cm,` `L_(3)=1/21**105=5cm` Hence the bridges should be placed at 75cm and `(75+25)=100cm`from one end.