Question

A string under a tension of $129.6N$ produces $10$ beats per sec when it is vibrated along with a tuning fork. When the tension in the string is increased to 160 N, it sounds in unison with the same tuning fork. The fundamental frequency of the tuning fork is

• A. $60Hz$
• B. $120Hz$
• C. $50Hz$
• D. $100Hz$

Answer 1

Answer: (D)

$100Hz$

Let $f,f_1,f_2$ are the fork frequency,initial and final frequencies of the string respectively.

Given : $|f-f_1|=10$ & $f=f_2$

We know that $f$ $\propto$ $\sqrt{T}$ for same no.of loops

Clearly $f_1$ is less than $f_2$ because frequency increases on increasing tension in the wire.

We have $\frac{f_1}{f_2}=\sqrt{\frac{T_1}{T_2}}$

$\frac{f-10}{f}=\sqrt{\frac{129.6}{160}}$

Solving we get $f=100Hz$

The fundamental frequency of tuning fork is $100Hz$.