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

Question

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 time t. Let ν p , ν Q a n d ν R be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 m s - 1 . Which of the following statement(s) is(are) true regarding the sound heard by the person ?

TestHub · Accepted Answer

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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