Question

Two tuning forks A & B produce notes of frequencies 256 Hz & 252 Hz respectively. An unknown note sounded at the same time 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. 260 Hz
• C. 250 Hz
• D. 242 Hz

Answer 1

Answer: (B)

260 Hz

we are given $n_A=256Hz$, $n_B=252Hz$, let us say the unknown freqency is $n_{unknown},$ then from the given conditions,

$n_{unknown}-n_A=a......................\left(1\right)$

$n_{unknown}-n_B=2a.......................\left(2\right)$

Now from $\left(2\right)/\left(1\right),$

$\frac{n_{unknown}-n_B}{n_{unknown}-n_A}=2$
$\frac{n_{unknown}-252}{n_{unknown}-256}=2$
$n_{unknown}=260Hz$

option "B" is correct.