JEE Advanced2016PhysicsWaves and SoundActual
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 ca
Options
- AThe rate of change in beat frequency is maximum when the car passes through Q
- Bν P + ν R = 2 ν Q
Correct answer
A. The rate of change in beat frequency is maximum when the car passes through Q
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