A sound source S and a detector D are located at some distance from each other. A large cardboard is placed near the detector, perpendicular to the line SD , as shown in the figure. The cardboard is gradually moved away, and it is observed that the intensity varies from a maximum to a minimum when the board is displaced by a distance of 20 cm . Determine the frequency of the emitted sound. The velocity of sound in ai

Step-by-step solution

Let the distance between the detector D and the cardboard be x . The sound waves reaching the detector consist of the direct wave from the source S and the reflected wave from the cardboard. The reflected wave travels an additional distance from the detector to the cardboard and back. Thus, the path difference between the direct and reflected waves is: p = 2x When the cardboard is displaced by a distance x = 20 cm , the new path difference becomes 2(x + x) . The change in the path difference is: p' = 2 x = 2 20 cm