Question

The two sources of sound, S1 and S2, emitting waves of 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 S1 S2 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 detector should be shifted to detect a minimum of sound.

Answer 1

Minimum Distance is 12 cm

Explanation:

Given,  

• Both the Sound Sources ($S_1 and S_2$), which are emitting equal wavelength (20.0 cm) waves, have a separation of 20.0 cm in between.

• Here, $\lambda$= 20 cm, $S_1S_2$= 20 cm, BD = 20 cm  

• Let the detector is shifted to left for a distance of x for hearing the lowest or minimum sound.

So path difference AL = BC - AB

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

So minimum distances for hearing -

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

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

• Hence,  

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

Which gives, x = 12 cm

* Refer Attached Figure