Question

Two sources of sound, $S_1$, and $S_2$, emitting waves equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to $S_1,S_2$ and at a distance of 20.0 cm 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 =20 cm

(Let the detector is shifted to left for a distance x for hearing the minimum sound)So path difference,

$\sqrt{A{B}^2+BC-AB}$

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

So the minimum distance hearing for minimum

$=\frac{(2n+1)\lambda }{2}=\frac{\lambda }{2}$

$=\frac{20}{2}=10cm$

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

Solving we get, x =12.0 cm