Question

Sound waves from a tuning fork $A$ reach a point $P$ by two separate paths $ABP$ and $ACP$. When $ACP$ is greater than $ABP$ by $11.5cm$, there is silence at $P$. When the difference is increased to $23cm$ the sound becomes loudest at $P$ and again when it increases to $34.5cm$ there is silence again and so on. Calculate the minimum frequency (in $Hz$ ) of the fork if the velocity of sound if taken to be $331.2m/s$.

Answer 1

Answer: 1440

Given that ${\Delta }_1=11.5cm=(2n+1)\frac{\lambda }{2}$ (Destructive)
and ${\Delta }_2=23cm=(2n+1)\lambda$ (Constructive)
${\Delta }_3=34.5cm=(2n+1)\frac{3\lambda }{2}$ (Destructive)
If there is no maxima or minima between ${\Delta }_1,{\Delta }_2$ and ${\Delta }_3$ that means $n=0$ for maximum wavelength or minimum frequency.
$\Rightarrow \frac{\lambda }{2}=11.5cm$
$\Rightarrow \lambda =23cm$
$\Rightarrow n=\frac{v}{\lambda }=\frac{331.2}{0.23}=1440Hz$