Question

Two sound waves emerging from a source reach a point simultaneously along two paths. When the path difference is 12 cm or 36 cm then there is silence at that point. If the speed of sound in air is 330 m/s then calculate least possible frequency of the source in Hz

Answer 1

For destructive interference : Path difference $\Delta x=(n+\frac{1}{2})\lambda$
Also, wavelength of wave $\lambda =\frac{v}{\nu }$
$\therefore$ We get $\nu =\frac{(2n+1)v}{2\Delta x}$
For least possible frequency, $n=0$ and $\Delta x=36cm$
$\therefore$ ${\nu }_{min}=\frac{1\times 330}{2\times 0.36}=458.33Hz$