Two loudspeakers M and N are 20 m apart and emit 118 Hz and 121 Hz. A car moves along the perpendicular bisector from P through midpoint Q to R at 60 km h⁻¹; P and R are each 1800 m from Q. Let ν(t) be the beat frequency in the car. Compare the beat frequencies at P, Q and R as indicated in the options. Take sound speed = 330 m s⁻¹.
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Question

Two loudspeakers M and N are 20 m apart and emit 118 Hz and 121 Hz. A car moves along the perpendicular bisector from P through midpoint Q to R at 60 km h⁻¹; P and R are each 1800 m from Q. Let ν(t) be the beat frequency in the car. Compare the beat frequencies at P, Q and R as indicated in the options. Take sound speed = 330 m s⁻¹.

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G1 Physics · Accepted Answer

Step 1: Beat frequency is fᵦ = |f₁ - f₂|. Step 2: Use how loading, shortening, tension change or motion changes the unknown frequency. Step 3: Select the value consistent with the stated increase/decrease of beat frequency. Final: A: Image 1; C: The rate of change in beat frequency is maximum when the car passes through Q; D: vP + vR = 2vQ.