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?

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.

To find the speed of the observer, we can use the Doppler effect equation:

f' = f * (v + vo) / (v + vs)

where:
f' is the observed frequency,
f is the source frequency,
v is the speed of sound in air,
vo is the speed of the observer, and
vs is the speed of the source (siren).

In this case, we are given the source frequency (f = 1099 Hz), and the observed frequency (f' = 1185 Hz). We also know that the speed of sound in air is constant (v = 343 m/s). We need to solve for the speed of the observer (vo).

We rearrange the Doppler effect equation to solve for vo:

f' * (v + vs) = f * (v + vo)

(f' * v + f' * vs) = (f * v + f * vo)

(f' * v - f * v) = (f * vo - f' * vs)

vo = ((f' * v - f * v) / f) + vs

Substituting the given values into the equation:

vo = ((1185 Hz * 343 m/s - 1099 Hz * 343 m/s) / 1099 Hz) + 0

vo = (406755 m/s - 377957 m/s) / 1099 Hz

vo = 288 m/s

Therefore, the speed of the observer is 288 m/s.