Question

An unknown frequency $x$ hertz produces $8$ beats per seconds with a frequency of $250Hz$ and $12$ beats with $270Hz$ source, then $x$ is

Answer 1

An unknown frequency $x$ hertz produces $8$ beats per seconds with a frequency of $250Hz$, therefore the possible frequencies are,

$250Hz\pm 8$
$258Hz$ or $242Hz$

As a source of frequency $270Hz$ gives $12$ beats per second. Therefore, the possible frequencies are,

$270Hz\pm 12$
$282Hz$ or $258Hz$

Therefore, the only possible frequency $x$ which gives $8$ beats with $250Hz$ and $12$ beats with $270Hz$ is $258Hz$.

Final Answer: $x=258Hz$