Question

Two tuning forks having frequency $256Hz\left(\right.A\left.\right)$ and $262Hz\left(\right.B\left.\right)$ . 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

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 $\left(1\right)$ ,
$f=f_{A}-f_{b}=258-6=252Hz$