Final answer:
The speed of the ambulance is approximately 1.61 m/s.
Step-by-step explanation:
The frequency of sound waves is affected by the relative motion between the source of the sound and the observer. This phenomenon is known as the Doppler effect. The frequency of sound heard by an observer will be different depending on whether the source of the sound is moving toward or away from the observer.
In this case, the cyclist hears a frequency of 1590 Hz after the ambulance passes. The original frequency emitted by the ambulance's siren is 1600 Hz. Since the cyclist hears a lower frequency, it indicates that the ambulance is moving away from the cyclist.
To find the speed of the ambulance, we can use the equation:
f' = f(v + vo) / (v - vs)
Where f' is the observed frequency, f is the original frequency, v is the speed of sound, vo is the velocity of the observer (in this case, the cyclist), and vs is the velocity of the source (the ambulance). Rearranging the equation, we can solve for vs:
vs = v((f/f') - 1) + vo
Plugging in the known values:
vs = (343 m/s)((1600 Hz/1590 Hz) - 1) + 2.44 m/s
vs = 1.61 m/s
Therefore, the speed of the ambulance is approximately 1.61 m/s.