Question

The length of a sonometer wire $AB$ is $110cm.$ 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)

Length of sonometer wire $(l)=110cm$
and ratio of frequencies $=1:2:3$.
Frequency $(v)\propto \frac{1}{l}$
or $l\propto \frac{1}{v}$.
Therefore $AC:CD:DB$
$=\frac{1}{1}:\frac{1}{2}:\frac{1}{3}=6:3:2$.
Therefore $AC=6\times \frac{110}{11}=60cm$ and
$CD=3\times \frac{110}{11}=30cm$.
Thus $AD=60+30=90cm$.