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 11.5 cm, there is silence at P. When the difference is 23 cm the sound becomes loudest at P and when 34.5 cm there is silence again and so on. Calculate the minimum frequency (in Hz) of the fork if the velocity of sound is taken to be 331.2 m/s.

Answer 1

When path difference =$11.5cm=\frac{\lambda }{2}(2n-1)$

Because there is silence at $P$ let $n=1$

$11.5=\frac{\lambda }{2}$

So, at $\frac{2}{\lambda }2$ there will be maxima.

and yes at $23cm$ there is maxima, at $3\lambda /2=34.5$

There is minima, so,

$\lambda =23cm$

$v=f\lambda$

$\frac{331.2}{23\times {10}^{-2}}=f=1440Hz$