A supersonic jet flies parallel to the ground with speed 0.75 Mach at height 1.5 km. Its engine frequency is ν₀ = 2 kHz. At some instant a ground observer hears frequency ν = 2ν₀. Find how long before hearing the sound was emitted. Take sound speed = 340 m s⁻¹.
Physics · Wave Motion
JEE Mains Advanced

Question

A supersonic jet flies parallel to the ground with speed 0.75 Mach at height 1.5 km. Its engine frequency is ν₀ = 2 kHz. At some instant a ground observer hears frequency ν = 2ν₀. Find how long before hearing the sound was emitted. Take sound speed = 340 m s⁻¹.

Physics · Wave Motion

G1 Physics · Accepted Answer

Step 1: For sound, f' = f(v ± vₒ)/(v ∓ vₛ), with velocities taken relative to the medium. Step 2: Choose signs for approach/recession; for an echo/reflection apply the Doppler shift twice. Step 3: If two frequencies are heard, take their difference for beats. Final: 5.9.