S 1 and S 2 are two identical sound sources of frequency 656 Hz . The source S 1 is located at O and S 2 moves anti-clockwise with a uniform speed 4 2 m s - 1 on a circular path around O , as shown in the figure. There are three points P , Q and R on this path such that P and R are diametrically opposite while Q is equidistant from them. A sound detector is placed at point P . The source S 1 can move along direction

Step-by-step solution

Given: f 0 = 656   Hz v = 324   m   s - 1 Frequency heard due to movement of ( S 1 ) f 1 = v v - u s f 0 ⇒ f 1 = 324 324 - 4 × 656 = 324 320 × 656 And frequency heard due to movement of ( S 2 ) would be same as that of f 0 , because the direction of velocity at position R is perpendicular to the line P R , so there is no relative change in position at that moment. f 2 = 656   Hz ∴ Beat frequency ∆ f = f 1 - f 2 = 656 324 320 - 1 ⇒ ∆ f = 8 . 2