Question

A source of sound with adjustable frequency produces $2$ beats per second with a tuning fork, when its frequency is either $466\text{Hz}$ or $470\text{Hz}$. What is the frequency of the tuning fork ?

• A. $466\text{Hz}$
• B. $470\text{Hz}$
• C. $468\text{Hz}$
• D. $472\text{Hz}$

Answer 1

The correct option is C $468\text{Hz}$

Let $f$ be the freqency of the tuning fork.
The frequency of sound source for which $2$ beats per second have been observed are,
$f_1=466\text{Hz}$ & $f_2=470\text{Hz}$
Therefore,
$|f-f_1|=2$
$\Rightarrow f-466=\pm 2$
$\Rightarrow f=468\text{Hz}\text{or}464\text{Hz}$
Similarly,
$|f-f_2|=2$
$\Rightarrow f-470=\pm 2$
$\Rightarrow f=472\text{Hz}\text{or}468\text{Hz}$
Since the same tuning fork has been used each time, hence on comparing ${}^{\prime }{f}^{\prime }$ we get:
$\Rightarrow f=468\text{Hz}$