Question

The frequency of a tuning fork ‘$x$’ is $5\%$ greater than that of a standard fork of frequency ‘$K$’. The frequency of another fork ‘$y$’ is $3\%$ less than that of ‘$K$’. When ‘$x$’ and ‘$y$’ are vibrated together $4$ beats are heard per second. The frequencies of $x$ and $y$ are

• A. 52.5Hz,48.5Hz
• B. 57.5Hz,47.5Hz
• C. 40.5Hz,42.5Hz
• D. 38.5Hz,48.5Hz

Answer 1

The correct option is A 52.5Hz,48.5Hz

Given : ${\delta }_x=\frac{105}{100}{\delta }_k$ and ${\delta }_y=\frac{97}{100}{\delta }_k$
Beat $={\delta }_x-{\delta }_y$
$4=\frac{105}{100}{\delta }_k-\frac{97}{100}{\delta }_k$
$4\times 100=8{\delta }_k$
${\delta }_K=50Hz$
${\delta }_x=\frac{105}{100}{\delta }_k$$=\frac{105}{100}\times 50$$=52.5Hz$
${\delta }_y=\frac{97}{100}\times {\delta }_k$$=\frac{97}{100}\times 50$$=48.5Hz$