Question

The frequency of a tuning fork $P$ is less by $1\%$ than the frequency of a standard tuning fork $S$ while the frequency of another tuning fork $Q$ is more by $2\%$ than the frequency of $S$. If $9$ beats/s are produced when $P$ and $Q$ are sounded together, the frequency of $P$ and $Q$ are respectively

• A. $148.5Hz,153Hz$
• B. $198Hz,204Hz$
• C. $297Hz,306Hz$
• D. $396Hz,408Hz$

Answer 1

The correct option is C $297Hz,306Hz$

Given : $\frac{{\delta }_p}{{\delta }_s}=\frac{99}{100}$ and $\frac{{\delta }_Q}{{\delta }_s}=\frac{102}{100}$

$Beats={\delta }_Q-{\delta }_P$

$9=\frac{102}{100}{\delta }_s-\frac{99}{100}{\delta }_s$

$\frac{9\times 100}{3}={\delta }_s$

$\Rightarrow {\delta }_s=300H_z$

${\delta }_P=\frac{99}{100}{\delta }_s$ $=\frac{99}{100}\times 300$ $=297H_z$

${\delta }_Q=\frac{102}{100}\times {\delta }_s$ $=\frac{102}{100}\times 300$ $=306H_z$