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?

Question

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.

Answer 1

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

Answer 2

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