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.
Answer & explanation
Correct answer: option 4
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,
$f_B'=f_A-3$
$=427-3$
$=424Hz$
$∴f_B=432Hz$