A stationary siren at ground level emits a short sound pulse toward a vertical cliff. A steady wind of speed 12m/s blows from the siren toward the cliff. The air temperature is 20∘C and the speed of sound relative to the air at this temperature is 343m/s.
(a) Derive an expression for the total time interval Δt between the emission of the pulse and the reception of its echo in terms of the actual distance d to the cliff, the still-air sound speed v, and the wind speed w when the wind blows from source to cliff.
(b) If the measured interval is 1.80s, calculate the true distance d to the cliff.
(c) Qualitatively describe how the value of d obtained from the same measured interval would differ if the wind direction were reversed while all other conditions remained unchanged.