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 $1sec$ . The frequency of the tuning fork $C$ is:-

• A. $200Hz$
• B. $240Hz$
• C. $360Hz$
• D. $300Hz$

Answer 1

Answer: (D)

$300Hz$

Given, the frequency of tuning fork A is $1.5\%$ more and that of B is $2.5\%$ less than C respectively and $f_A-f_B=12Hz$

Find the frequency of C.

Let us suppose that the frequency of C is $f$.

Then, $f_A=f+\frac{1.5}{100}f\&f_B=f-\frac{2.5}{100}f$

$f_A=\frac{203f}{200}\&f_B=\frac{195f}{200}$

As given, $f_A-f_B=\frac{203f}{200}-\frac{195f}{200}=12Hz$

$\Rightarrow \frac{8f}{200}=12Hz$

$\Rightarrow f=\frac{12\times 200}{8}=300Hz$

So, D is the correct answer.