The siren of an ambulance has a frequency f=500 Hz. A pedestrian standing on a
sidewalk listens to this siren as the ambulance passes by at a speed of 65 mph. The speed
of sound in air is 330 m/s.
a) Calculate the total shift in frequency detected by the pedestrian as the ambulance
passes.
Va = 65mi/h * 1600m/mi * 1h/3600s = 28.9 m/s.
F1 = (Vs+Vp)/(Vs-Va) * Fa.
F1 = (330+0)/(330-28.9) * 500 = 548.0 Hz.
F2 = (330-0)/(330+28.9) * 500 = 459.7 Hz.
F1-F2 = 548 - 459.7 = 88.3 Hz. = Total shift in freq.
To calculate the total shift in frequency detected by the pedestrian as the ambulance passes, we need to consider the phenomenon known as the Doppler effect.
The Doppler effect describes the change in frequency of a wave (in this case, sound) as the source (the ambulance) and the observer (the pedestrian) move relative to each other. When the source is moving towards the observer, the observer detects a higher frequency (known as a blue shift). When the source is moving away from the observer, the observer detects a lower frequency (known as a red shift).
In this case, the ambulance is moving towards the pedestrian. To calculate the total shift in frequency, we can use the Doppler effect equation:
Δf = (v / v_sound) * f
Where:
Δf is the change in frequency detected by the observer,
v is the speed of the source (the ambulance),
v_sound is the speed of sound in air, and
f is the frequency of the source (the siren).
Given:
v = 65 mph = 29.1 m/s (since 1 mph = 0.447 m/s)
v_sound = 330 m/s
f = 500 Hz
Plugging in the values:
Δf = (29.1 / 330) * 500
Δf = 4.31 Hz
Therefore, the total shift in frequency detected by the pedestrian as the ambulance passes is 4.31 Hz.