Question

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

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

Answer 1

Answer: (B)

$1000Hz$

Answer is B
Since the length of sonometer is divided in the ratio $6:3:2$, than the maximum wavelength is
$\lambda =\frac{2}{11}\times 110=20cm$
Now, speed of waves on a string is
$V=\sqrt{\frac{T}{\mu }}$
and,
frequency, $f=\frac{1}{\lambda }\sqrt{\frac{T}{\mu }}$
$f=\frac{100}{20}\sqrt{400\times 100}$
$f=1000Hz$