Question

Two sources of sound, $S_1$ and $S_2$, emitting waves of equal wavelength $20.0cm$, are placed with a separation of $20.0cm$ between them. A detector can be moved on a line parallel to $S_1{S}_2$ and at a distance of $20.0cm$ from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through which the detector should be shifted to detect a minimum of sound.

Answer 1

According to the data

$\lambda =20cm,S_1{S}_2=20cm,BD=20cm$

Let the detector is shifted to left for a distance $x$ for hearing the minimum sound

So path difference $AI=BC-AB$

$=\sqrt{(20{)}^2+(10+x{)}^2}-\sqrt{(20{)}^2+(10-x{)}^2}$

So the minimum distance hearing for minimum

$AI=\frac{(2n+1)\lambda }{2}=\frac{\lambda }{2}=\frac{20}{2}=10cm$

Substitute the value in equation of path difference:

$\Rightarrow \sqrt{(20{)}^2+(10+x{)}^2}-\sqrt{(20{)}^2+(10+x{)}^2}=10$

solving we get $x=12.0cm$