Question

The frequencies of two tuning forks $A$ and $B$ are respectively $1.5\%$ more and $2.5\%$ less than that of the tuning fork $C$. When $A$ and $B$ are sounded together, $12$ beats are produced in $1\sec$. The frequency of the tuning fork $C$ is

• A. 200 Hz
• B. 240 Hz
• C. 360 Hz
• D. 300 Hz
• E. 400 Hz

Answer 1

Answer: (D)

Let the frequency of tuning fork $C$ is $xHz$.
The frequency of tuning fork $A$ is
$x+\frac{1.5}{100}x=1.015x$
The frequency of tuning fork $B$ is $x-\frac{2.5}{100}x$
$=0.975x$
Beat frequency of tuning fork $A$ and $B$ is
$1.015x-0.975x=0.04x$
Thus, $0.04x=12$
$\Rightarrow x=\frac{12}{0.04}=300Hz$