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JEE Advanced Physics Waves and Sound 2023 JEE Advanced 2023 (Paper 2)

JEE Advanced Physics Question (2023) — Solution

Question

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 O P . [Given: The speed of sound in air is 324   m   s − 1 ] Consider both sources emitting sound. When  S 2  is at R and  S 1  approaches the detector with a speed  4   m   s - 1 , the beat frequency measured by the detector is _____  Hz .

Options

  1. A. A
  2. B. B
  3. C. C
  4. D. D

Answer

A. A

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

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