The frequency F of a fire truck siren heard by a stationary observer is given be
ID: 2861071 • Letter: T
Question
The frequency F of a fire truck siren heard by a stationary observer is given below, where ± v represents the velocity of the accelerating fire truck in meters per second (see figure). (Round your answers to 3 decimal places). F = 131,000/319 ± v
(a) Find the rate of change of F with respect to v when the fire truck is approaching at a velocity of 24 meters per second (use v).
F'(24) =
(b) Find the rate of change of F with respect to v when the fire truck is moving away at a velocity of 24 meters per second (use +v).
F'(24) =
Explanation / Answer
a)F = 131,000/(319 - v)
F' = [-131,000/(319 - v)2]*(0-1)
F' = 131,000/(319 - v)2
F'(-24) = 131,000/(319 - (24))2
F'(-24) =1.505
b)F = 131,000/(319 + v)
F' = -131,000/(319 + v)2
F'(24) = -131,000/(319 + (24))2
F'(24) =-1.114
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