Question

Two tuning forks having frequency $256Hz(A)$ and $262Hz(B)$ . Tuning fork $A$ produces some beats per second with unknown tuning fork, same unknown tuning fork produce double beats per second from $B$ tuning fork, then the frequency in $Hz$ of unknown tuning fork is:-

Answer 1

Answer: 252

Given, $f_A=256Hz$ , $f_B=262Hz$
Let the frequency of the unknown tuning fork is $f$ .
If the tuning fork produce $f_b$ beats with $A$ , it will produce $2f_b$ beats with $B$ .
So, $f_A-f=f_b...\left(1\right)$
and $f_B-f=2f_b...\left(2\right)$
From $\left(2\right)-\left(1\right)$ ,
$f_B-f_A=f_b\Rightarrow 262-256=f_b\Rightarrow f_b=6Hz$
From equation $\left(1\right)$ ,
$f=f_A-f_b=258-6=252Hz$