The Doppler effect is a change in the observed frequency of a wave (such m a sound wave or light wave) when the source of the wave and observer are in motion relative to each other. The Doppler effect explains why an observer hears a change in pitch of an ambulance siren as the ambulance passes by the observer. The frequency F v 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 sound in air (772.4 mph). and v is the speed at which the source of sound is moving toward the observer. Use this relationship for Exercises 99-100. Suppose the frequency of sound emitted by a police car siren is 600 Hz. a. Write F as a function of v if the police car is moving toward an observer. b. Suppose that the frequency of the siren as heard by an observer is 664 Hz. Determine the velocity of the police car. Round to the nearest tenth of a mph. c. Although a police car cannot travel dose to the speed of sound. interpret the meaning of the vertical asymptote
The Doppler effect is a change in the observed frequency of a wave (such m a sound wave or light wave) when the source of the wave and observer are in motion relative to each other. The Doppler effect explains why an observer hears a change in pitch of an ambulance siren as the ambulance passes by the observer. The frequency F v 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 sound in air (772.4 mph). and v is the speed at which the source of sound is moving toward the observer. Use this relationship for Exercises 99-100. Suppose the frequency of sound emitted by a police car siren is 600 Hz. a. Write F as a function of v if the police car is moving toward an observer. b. Suppose that the frequency of the siren as heard by an observer is 664 Hz. Determine the velocity of the police car. Round to the nearest tenth of a mph. c. Although a police car cannot travel dose to the speed of sound. interpret the meaning of the vertical asymptote
Solution Summary: The author explains the function F of v given that the actual frequency of sound emitted by the car siren is 600Hz when an ambulance is moving towards an observer.
The Doppler effect is a change in the observed frequency of a wave (such m a sound wave or light wave) when the source of the wave and observer are in motion relative to each other. The Doppler effect explains why an observer hears a change in pitch of an ambulance siren as the ambulance passes by the observer. The frequency
F
v
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 sound in air (772.4 mph). and v is the speed at which the source of sound is moving toward the observer. Use this relationship for Exercises 99-100.
Suppose the frequency of sound emitted by a police car siren is 600 Hz.
a. Write F as a function of v if the police car is moving toward an observer.
b. Suppose that the frequency of the siren as heard by an observer is 664 Hz. Determine the velocity of the police car. Round to the nearest tenth of a mph.
c. Although a police car cannot travel dose to the speed of sound. interpret the meaning of the vertical asymptote
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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