Final answer:
To find the speed of the ambulance, we can use the Doppler effect equation and the given frequencies and speeds. Plugging in the values and solving for the source's speed, we find that the speed of the ambulance is approximately 340.07 m/s.
Step-by-step explanation:
The question involves the Doppler effect, which describes how the frequency of a sound wave appears to change when the source of the wave is moving relative to an observer.
Given that the speed of sound is 340 m/s and the observer hears a frequency of 1022 Hz while the ambulance is approaching, and a frequency of 981 Hz after the ambulance has passed, we can use the Doppler effect equation to find the speed of the ambulance.
The Doppler effect equation for sound is given by:
f' = f((v + vo)/(v - vs))
Where f is the source frequency, f' is the perceived frequency, v is the speed of sound, vo is the observer's speed, and vs is the source's speed.
In this case, the source frequency f is 1022 Hz, the perceived frequency f' is 981 Hz, the speed of sound v is 340 m/s, and the observer's speed vo is 15.0 m/s (since they are driving at a speed of 15.0 m/s).
Plugging in these values into the Doppler effect equation and solving for vs, we can find the speed of the ambulance:
981 = 1022((340 + 15)/(340 - vs))
Simplifying the equation:
340 + 15 = 1022(340 - vs)
355 = 347780 - 1022vs
1022vs = 347780 - 355
1022vs = 347425
vs = 347425/1022
vs ≈ 340.07 m/s