The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
Solution Summary: The author explains the cost function F of v if the actual frequency of sound emitted by the ambulance is 560Hz.
The function F of v if the actual frequency of sound emitted by the ambulance is 560Hz when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by Fv=fas0s0−v , where fa is the actual frequency of the sound at the source, s0 is the speed of the sound in air 772.4mph , and v is the speed at which the source of sound is moving toward the observer.
(b)
To determine
To graph: The sketch of a function given by Fv=560772.4772.4−v on the window 0,1000,100by0,5000,1000 .
(c)
To determine
The effect of the frequency of sound when the speed of the ambulance increases.
Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by
Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves
Nolan's hand and the angle 0 above the horizontal at which it is thrown.
SPEED v (ft/s)
80
85
90
95
35
188
212
238
266
40
197
222 249
278
45
200 226 253
281
50
197
222
249
278
Use the accompanying table and the equations below to estimate the stated partial derivatives.
f(хо + Дх, Уо) -f (хо- Уo)
if,(xo, yo) = lim
Ay-0
f (x0, Yo + Ay) – f (xo. Yo)
Ay
f. (xo, Yo) = lim
Ax-)
Ax
Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer.
(a) Estimate the partial derivative of r with respect to v when v = 85ft/s and 0 = 45°.
dr
i
dv
(b) Estimate the partial derivative of r with respect to 0 when v = 85ft/s and e = 45°.
dr
ANGLE O (degrees)
When the source of the sound is moving away from the observer, the equation that describes this
C
phenomenon is f
fo, where
c + v
fis the observed frequency (pitch) of the sound, in Hertz
c is the speed of sound, in miles per hour (about 761 miles per hour)
v is the speed of the sound source, in this case the car, in miles per hour
fo is the frequency of the sound when stationary
Using a spectrum analyzer, we could determine the observed frequency when the car was driving
towards us was 270 Hz and the frequency while driving away was 240 Hz, suggesting a stationary
frequency of 255 Hz.
Use this information and the equation to estimate the speed of the car in miles/hour. Round your
answer to one decimal place.
mi/hr
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