Question

The tuning forks A and B produce notes of frequency $256$ Hz and $262$ Hz respectively. An unknown note sounded at the sametime as A produces beats. When the same note is sounded with B, beat frequency is twice as large. The unknown frequency could be:

• A. 268 Hz
• B. 250 Hz
• C. 260 Hz
• D. None of these

Answer 1

The correct option is B 250 Hz

$a$ is the +ve constant
$\left(I\right)256+a=262-2a$ $=f_0\Rightarrow a=2$
$f_0=258Hz$
$\left(II\right)256+a=262+2a=f_0$
Not Possible
$\left(III\right)256+a=262+2a=f_0$
Not possible a have -ve value
$\left(IV\right)256-a=262-2a=f_0\Rightarrow a=6$
$f_0=250Hz$