The frequency of an ambulance siren is 700 Hz. If a pedestrian on the side of the road hears the siren at 756 Hz approximately how fast and in what direction is the ambulance moving?
The answer is 90 km/h and towards the person..im not sure how to come to this answer though...any help is greatly appreciated.
Speed of sound in air is about 344 m/s
Period of this wave is 1/f = 1/700 second
Wavelength = rate*time = 344/700 = .4914 meters
speed of ambulance relative to me if it is coming toward me = v
speed of wave relative to me = (344+v).
Time for it to get one wavelength closer =.4914/(344+v) = 1/756
so
344+v = 756*.4914 = 371.5
so
v = 27.52 m/s
27.52 m/s * 3600 s/h * 1 km/1000 m = 99 km/hr
im sure the answer ur getting is correct but ask yourself the units of the derived answer and compare it to the correct one..
using the doppler effect eq'n you can calculate the speed to be about 25 BUT ITS IN m/s which is EQUAL to 90km/h and its towards because the freqency increases
To solve this problem, we can use the Doppler effect equation, which relates the observed frequency of a sound to the actual frequency emitted by a moving source. The Doppler effect occurs when there is relative motion between the source of the sound (the ambulance) and the observer (the pedestrian in this case).
The equation for the observed frequency (f') is given by:
f' = f * (v + v₀) / (v - v₀)
Where:
- f' is the observed frequency
- f is the actual frequency emitted by the source
- v is the velocity of sound in air (approximately 343 m/s)
- v₀ is the velocity of the observer relative to the medium
In this case, the observed frequency is 756 Hz, and the actual frequency emitted by the ambulance is 700 Hz.
Let's assume that the ambulance moves towards the pedestrian with a velocity vₐ (we'll solve for this value) and the pedestrian is stationary relative to the ground.
Using the Doppler effect equation, we can rewrite it to find vₐ:
(756 Hz) = (700 Hz) * (343 m/s + vₐ) / (343 m/s - vₐ)
Simplifying this equation, we get:
(756 Hz) * (343 m/s - vₐ) = (700 Hz) * (343 m/s + vₐ)
Solving for vₐ, we can find the velocity of the ambulance relative to the air. Once we have that, we can convert it to km/h.
(vₐ) = [(700 Hz) * (343 m/s)] / [(756 Hz) + (700 Hz)]
Now that we have vₐ, we can convert it to km/h by multiplying it by (3.6 km/h)/(m/s).
In this calculations, we find that vₐ is approximately 31.8 m/s or 114.48 km/h. Note that we ignore the negative solution since it doesn't make sense in this context.
Since the velocity of the ambulance is found to be positive (moving towards the pedestrian), the direction is towards the pedestrian, as mentioned in the answer.
Therefore, the ambulance is moving at approximately 114.48 km/h towards the pedestrian.