Question

A tuning fork produces $8$ beats /s with a sonometer wire. When tension in the wire is increased by $21$% again $8$ beats/s produced with the same tuning fork, the frequency of the tuning fork is

• A. $168Hz$
• B. $176Hz$
• C. $328Hz$
• D. $336Hz$

Answer 1

Answer: (A)

$168Hz$

From first condition,

$f_{tf}-f_{sono}=8$ ....(1)

From second condition,

$-f_{tf}+f_{sono}^{\prime }=8$ ....(2)

$\frac{f_{sono}^{\prime }}{f_{sono}}=\sqrt{\frac{1.21T}{T}}=1.1$

$f_{sono}^{\prime }=1.1\times f_{sono}$

Now add equation $\left(1\right)$ and $\left(2\right)$, and substituting value of $f_{sono}^{\prime }$, we will get:

$f_{sono}=160Hz$

And from equation $\left(1\right)$,

$f_{tf}=168Hz$