Travelling along a straight line at a speed of 170 m s ⁻¹ , a source of sound emits a 1200 Hz note. A detector is located 200 m away from the source's line of motion. Determine the distance separating the source and the detector at the instant the detector registers a frequency of 1200 Hz . Assume the velocity of sound in air to be 340 m s ⁻¹ .

Step-by-step solution

The apparent frequency registered by the detector is given by the Doppler effect formula: f = f₀ ( v v - v_s ) where v is the velocity of sound, v_s is the velocity of the source, and is the angle between the source's velocity vector and the line joining the source to the detector at the instant the sound is emitted. Given that the emitted frequency f₀ = 1200 Hz and the registered frequency f = 1200 Hz , we have: 1200 = 1200 ( v v - v_s ) v - v_s = v = 0 = 90^ This means the sound heard by the detector was emitted