Q.

The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1: 3: 5.

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a

30023 cm,150023 cm

b

150023 cm,200023 cm

c

150023 cm,50023 cm

d

150023 cm,30023 cm

answer is D.

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Detailed Solution

 Let L(=100 cm) be the length of the wire and L1,L2 and L3 are the lengths of the segments as shown in the figure. 

Question Image

 Fundamental frequency, ν1L  As the fundamental frequencies are in the ratio of 1:3 : 5,  L1:L2:L3=11:13:15=15:5:3 

 Let x be the common factor. Then, 15 x+5 x+3 x=L=100 23x=100  or,  x=10023;

 L1=15×10023=150023 cm ;         L2=5×10023=50023 cm ;         L3=3×10023=30023 cm ;

 The bridges should be placed from A  at 150023 cm and 200023 cm respectively. 

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