Question

The frequency of tuning forks $A$ and $B$ are respectively $3\%$ more and $2\%$ less than the frequency of the tuning fork $C$. When $A$ and $B$ are simultaneously excited then $5$ beats per second are produced. The frequency of the tuning fork $A$ is

• A. $109\text{Hz}$
• B. $107\text{Hz}$
• C. $105\text{Hz}$
• D. $103\text{Hz}$

Answer 1

The correct option is D $103\text{Hz}$

Let us suppose, the frequency of the tuning fork $C$ is $f$.
Then, the frequency of the tuning fork $A$ will be,
$f_A=1.03f$ and
of tuning fork $B$ will be,
$f_B=0.98f$
Now, beat frequency,
$f_b=|f_A-f_B|$
$\Rightarrow 5=1.03f-0.98f$
$\Rightarrow f=100\text{Hz}$
Hence, the frequency of tuning fork $A$ is $f_A=1.03f=103\text{Hz}$