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NEETPhysicsWaves and Sound

Two loudspeakers M and N are located 20m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let υ t represent the beat frequency measured by a person sitting in the car at

Options

  1. AThe rate of change in beat frequency is maximum when the car passes through Q
  2. BNone of the above

Correct answer

3

Step-by-step solution

f M = C + V cos ⁡ θ C f 1 f N = C + V cos ⁡ θ C f 2 Δ f = f N - f M = C + V cos ⁡ θ C f 2 - f 1 d Δ f d t = - V C f 2 - f 1 sin ⁡ θ d θ d t ∴ and d Δ f d t is maximum when θ = 90 o ∴ i i i i s c o r r e c t v P = 1 + V C cos ⁡ θ Δ f v Q = Δ f v R = 1 - V C cos ⁡ θ Δ f ∴ v P + v r = 2 v Q

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