Two sitar stings A and B playing a note are slightly out of tune and produces beats of frequency 5 Hz. The tension in string B is slightly increased and beat frequency become 3 Hz. What is the original frequency of B if frequency of A is 427 Hz.

422 Hz

The correct answer is Option (4) → 422 Hz

The beat frequency $f_{beat}$ is -

$f_{beat}=|f_A-f_B|=5$

$f_B=f_A+5$

$=427+5$

$=432Hz$

or, 

$f_B=f_A-5$

$=427-5$

$=422Hz$

Now,

$|f_A-f_B'|=3$

$f_B'=f_A+3$

$=427+3$

$=430Hz$

or,

$f_B'=f_A-3$

$=427-3$

$=424Hz$

$∴f_B=432Hz$