The speed of the ambulance is 4.61 m/s.
Doppler's effect formula is used, which is
[tex]f' = f (\frac{v + vo}{v + vs})[/tex]
Where,
f' = observer frequency of sound
f = actual frequency of sound waves
v = speed of sound waves
vo = velocity of observer
vs = velocity of source
Here, observer is the cyclist and source is the ambulance.
Given,
f' = 1590 Hz
f = 1600 Hz
v = 343 m/s
vo = 2.44 m/s
Now put the given values in the above formula,
[tex]f' = f (\frac{v + vo}{v + vs})[/tex]
[tex]1590 = 1600 (\frac{343 + 2.44}{343 + vs})[/tex]
[tex]1590 = 1600( \frac{345.44}{343 + vs})[/tex]
[tex]1590 = \frac{552,704}{343+vs}[/tex]
[tex]343+vs = \frac{552,704}{1590\\}[/tex]
[tex]343 + vs = 347.61\\[/tex]
[tex]vs = 347.61 - 343[/tex]
[tex]vs = 4.61 m/s[/tex]
Hence, the speed of the ambulance is 4.61 m/s.
Learn more about doppler effect here:
https://brainly.com/question/1330077
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