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

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

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Solution:

Since source of frequency $x$ gives 8 beats per second with frequency $250\, Hz$, its possible frequency are 258 or $242 .$ As source of frequency $x$ gives 12 beats per second with a frequency $270\, Hz$, its possible frequencies 282 or $258\, Hz$. The only possible frequency of $x$ which gives 8 beats with frequency $250\, Hz$ also 12 beats per second with $258\, Hz$.