Problem 53059. Siren frequency and Doppler effect.

Created by Gerard Stockil

Difficulty:Rate

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The Doppler effect is described on OpenStax University Physics at https://openstax.org/books/university-physics-volume-1/pages/17-7-the-doppler-effect and in other sources.  
Consider the  Doppler effect for sound waves travelling in air.  Use the equations in the OpenStax source (or equivalent information ) to model the Doppler effect. 
A moving vehicle with a speed u, having a siren frequency, fs, approaches a static (fixed)  observer and then passes the static observer.   A siren , in this context,  is also called a horn.  The vehicle motion is modelled as straight-line motion. 
One way of summarising the effect to the formula for two frequencies
  
or written in MATLAB syntax as
fh = fs *(c/(c-u)) 
fl = fs *(c/(c+u)) 
where fs is the frequency of a siren in Hz,  c is the  speed of sound in m/s , u is the speed of the moving vehicle in m/s,  fh is the higher frequency in Hz as the vehicle approaches the  stationary observer and the fl the lower frequency  in Hz as the vehicle recedes from (passes) the observer. 
Calculate the siren frequency, fs, to the nearest Hz.  The function definition is 
fs = findSirenFrequency ( c, u, fh, fl )
For example, if  c = 345  m/s  ; u= 30.5556 m/s ;  fh = 877  Hz and fl =734 Hz   then fs= 799 Hz.   Assume  fh ≥ fl and c > u.
 

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