Question

The length of a sonometer wire $AB$ is 110 cm. Where should the two bridges be placed from A to divide the wire in three segments whose fundamental frequencies are in the ratio of 1:2:3

• A. 30 cm and 90 cm
• B. 40 cm and 80 cm
• C. 60 cm and 90 cm
• D. 30 cm and 60 cm

Answer 1

Answer: (C)

60 cm and 90 cm

Answer 2

Fundamental frequency $f \propto \frac{1}{l}$

Given, $f_1 : f_2 :f_3 = 1 : 2 : 3$
or $\frac{1}{l_1} : \frac{1}{l_2} : \frac{1}{l_3} = 1 : 2 : 3$
or $l_1 : l_2 : l_3 = \frac{1}{1} : \frac{1}{2} : \frac{1}{3}$
or $l_1 : l_2 : l_3 = 6: 3 : 2$
$l_1 = \frac{6}{11} \times 110 = 60 \, cm$
$l_2 = \frac{3}{11} \times 110 = 30 \, cm$
and $l_3 = \frac{2}{11} \times 110 = 20 \, cm$