MCQ
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 ........... $Hz$ ?
  • A
    $1100$
  • $1000$
  • C
    $166$
  • D
    $100$

Answer

Correct option: B.
$1000$
b
Total length of sonometer wire, $l=110 \mathrm{cm}$ $=1.1 \mathrm{m}$

Length of wire is in ratio,$6: 3: 2$ i.e $60 \mathrm{cm}$, $30 \mathrm{cm}, 20 \mathrm{cm}$

Tension in the wire, $T=400 \mathrm{N}$

Mass per unit length, $\mathrm{m}=0.01 \mathrm{kg}$

Minimum common frequency $=?$

As we know,

Frequency, $v=\frac{1}{21} \sqrt{\frac{T}{m}}=\frac{1000}{11}-H z$

Similarly, $v_{1}=\frac{1000}{6} \mathrm{Hz}$

$v_{2}=\frac{1000}{3} \mathrm{Hz}$

$v_{3}=\frac{1000}{2} \mathrm{Hz}$

Hence common frequency $=1000 \mathrm{Hz}$

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