Problem: A sound with a 40.0cm wavelength travels rightward from a source and th

Question

Problem: A sound with a 40.0cm wavelength travels rightward from a source and througha tube that consists of a straight portion and a half-circle. Part of the sound wave travels through the half-circle andthen rejoins the rest of the wave, which goes directly through thestraight portion. This rejoining results ininterference. What is the smallestradius r that results in an intensity minimum atthe detector? I knowthat = (L / )(2),and that so far I havegotten = [r ( - 2)]/ 40.0 I do not know what to do from here though. Itsays in the solution that in order to obtain the minimumradius, must equal , and that bysubstituting into the above equation, I am able tosolve for r. I am confused, however, as tohow must equal in order for theradius to be minimized. How do I knowthat must equal ? Problem: A sound with a 40.0cm wavelength travels rightward from a source and througha tube that consists of a straight portion and a half-circle. Part of the sound wave travels through the half-circle andthen rejoins the rest of the wave, which goes directly through thestraight portion. This rejoining results ininterference. What is the smallestradius r that results in an intensity minimum atthe detector? I knowthat = (L / )(2),and that so far I havegotten = [r ( - 2)]/ 40.0 I do not know what to do from here though. Itsays in the solution that in order to obtain the minimumradius, must equal , and that bysubstituting into the above equation, I am able tosolve for r. I am confused, however, as tohow must equal in order for theradius to be minimized. How do I knowthat must equal ?

Explanation / Answer

The intensity is minimum indicated that at the detector, there aredestructive interference. So for 2 wave be able to have a destructive interference, thedifference is phase is . That is the reason why is the magnitude of the angle.

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