a siren has a frequency of 1099 Hz when it and an observer are both at rest. The observer then starts to move and finds that the frequency he hears is 1185 Hz. What is the speed of the observer?

Answer 1

Fo = ((Vs+Vo)/(Vs-Vg))*Fg = 1185 Hz
((343+Vo)/(343-0))*1099 = 1185
((343+Vo)/343)*1099 = 1185
Multiply both sides by 343/1099:
343 + Vo = 1185 * 343/1099 = 369.8
Vo = 369.8 - 343 = 26.84 m/s = Velocity
of the observer.