The length of the wire between two ends of a sonometer is 100cm. What should be the positions of two bridges (from left end of sonometer) below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1:3:5
A
150023cm,50023cm
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B
150023cm,30023cm
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C
30023cm,80023cm
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D
150023cm,200023cm
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Solution
The correct option is D150023cm,200023cm Let L(=100cm) be the length of the wire and L1,L2 and L3 are the lengths of the segments as shown in the figure.
Fundamental frequency, f∝1L
As the fundamental frequencies are in the ratio of 1:3:5, ∴L1:L2:L3=11:13:15=15:5:3
As L=L1+L2+L3
Let x be the common factor. Then 15x+5x+3x=100 23x=100 x=10023