Question

The total length of a sonometer wire between fixed ends is $110\, cm$. Two bridges are placed to divide the length of wire in ratio $6 : 3 : 2$. The tension in the wire is $400\, N$ and the mass per unit length is $0.01\, kg/m$. What is the minimum common frequency with which three parts can vibrate ?

• A. 1100 Hz
• B. 1000 Hz
• C. 166 Hz
• D. 100 Hz

Answer 1

Answer: (B)

1000 Hz

Answer 2

$\ell_{1}: \ell_{2}: \ell_{3}=6: 3: 2$ so $\ell_{1}=60 \,cm$ $\ell_{2}=30 \,cm$ $\ell_{3}=20 \,cm$ $60,30,20$ $\frac{\lambda}{2}=10\,cm$ $f =\frac{200}{2}$ $=1000\,Hz$