Question

(2) While out on a call for GERMS, an EMT hears the sound of an ambulance ap- proaching. The EMT is completely stationary. It is quite an emergency, so the ambulance is approaching at 55 mph and emitting its siren at a frequency of 1200 Hz. (a) What is the frequency heard by the EMT? (b) What is the frequency heard by the hospital away from which the ambulance is moving? (c) What is the frequency of the echo off the hospital heard by the person driving the ambulance? That is, the sound has left the siren, bounced off of the hospital, and returned to the driver in the moving ambulance.

Answer 1

The doppler shift due to relative motion b/w source and observer is n_eff = (v plusminus v_0/v plusminus v_s)n Here v is velocity of sound of air, v_0 is velocity of observer and v_s is the velocity of the source and n is the natural frequency of source a) If the observer (EMT) is stationary and source (ambulance) moves towards observer n_eff = n(v/v - v_s) here velocity of ambulance, v_s = 55 mph(0.447 m/s/mph) = 24.585 m/s therefore n_eff = (1200 Hz)(343 m/s/343 m/s - 24.585 m/s) almostequalto 1293 Hz b) If the (EMT) is stationary and source (ambulance) moves away from observer n_eff = n(v/v + v_s) = 1200 Hz(343 m/s/343 m/s + 24.585 m/s) almostequalto 1120 Hz c) n_eff = (v + v_s/v - v_s)n = 1200 Hz(343 m/s + 24.585 m/s/343 m/s - 24.585 m/s) almostequalto 1385 Hz