Question

A tuning fork is in resonance with a sonometer wire. The same tuning fork produces 3 beats in $2s$ when the tension in the wire is increased by $2\%$. The frequency of wire before increasing tension is:

• A. $100Hz$
• B. $150Hz$
• C. $200Hz$
• D. $300Hz$

Answer 1

Answer: (B)

$150Hz$

Given :$\frac{T_1}{T_2}=\frac{100}{102}$
Beat $=\frac{3}{2}$
$\delta \alpha \sqrt{T}$
$\frac{{\delta }_1}{{\delta }_2}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{100}{102}}$
$\Rightarrow {\delta }_1={\delta }_2\sqrt{\frac{100}{102}}\Rightarrow {\delta }_2=\sqrt{\frac{102}{100}}{\delta }_1$---(!)
Now, Beat $={\delta }_2-{\delta }_1$
So, $\frac{3}{2}={\delta }_1\sqrt{\frac{102}{100}}-{\delta }_1$ (from (1))
or, $\frac{3}{2}={\delta }_1(\sqrt{\frac{102}{100}}-1)$
$\Rightarrow {\delta }_1=\frac{3}{2}\times \frac{1}{(\sqrt{\frac{102}{100}}-1)}$$=150Hz$