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Old 04-20-2013   #2
MAS1

 
Join Date: Dec 2008
Posts: 249
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Quote:
Originally Posted by Denise44 View Post
The Doppler Effect (named after Christian Doppler) is the change in the pitch (frequency) of the sound from a source (s) as heard by an observer (o) when one or both are in motion. If we assume both the source and the observer are moving in the same direction, the relationship is: f' = fa(v-vo/v-vs)

where f' = perceived pitch by the observer
fa = actual pitch of the source
v = speed of sound in air (assume 772.4 mph)
vo = speed of the observer
vs = speed of the source

Suppose you are traveling down the road at 45 mph and you hear an ambulance (with siren) coming toward you from the rear. The actual pitch of the siren is 600 hertz.

a) Write a function f'(Vs) that describes this scenario.

b) If f' = 620 Hz, find the speed of the ambulance.
a) f'(vs) = 600((772.4 - 45)/(772.4 - vs))

b) 620 = 600((772.4 - 45)/(772.4 - vs))
(620/600) = (727.4/(772.4 - vs))
1.0333 = 727.4/(772.4 - vs)
31/30 = 727.4/(772.4 - vs)
Cross multiplying gives:
(30)(727.4) = (31)(772.4 - vs)
21822 = 23944.4 - 31vs
31vs = 2122.4
vs = 68.465 mph
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