To determine the ambulance's speed, we can use the formula that relates the observed frequency of sound (f_o) to the actual frequency (f_s), the speed of sound (v), and the speed of the observer/source (v_o/s):

f_o = f_s * v / (v +/- v_o/s)

In this case, the observed frequency (f_o) is 645 Hz, the actual frequency (f_s) of the ambulance's siren is typically around 440 Hz, the speed of sound (v) is approximately 343 m/s, and since the ambulance is moving towards us, v_s is negative.

So, plugging in the values:

645 Hz = 440 Hz * 343 m/s / (343 m/s - v_s)

Solving for v_s:

v_s = 343 m/s - (440 Hz / 645 Hz) * 343 m/s

v_s ≈ 343 m/s - (0.68 / 1.36) * 343 m/s

v_s ≈ 343 m/s - 0.5 * 343 m/s

v_s ≈ 343 m/s - 171.5 m/s

v_s ≈ 171.5 m/s

Therefore, the ambulance is approaching at a speed of approximately 171.5 meters per second.