(III) A radar “speed gun” emits microwaves of frequency f 0 = 36.0 GHz. When the gun is pointed at an object moving toward it at speed v , the object senses the microwaves at the Doppler-shifted frequency f . The moving object reflects these microwaves at this same frequency f . The stationary radar apparatus detects these reflected waves at a Doppler-shifted frequency f ′. The gun combines its emitted wave at f 0 and its detected wave at f ′. These waves interfere, creating a beat pattern whose beat frequency is f beat = f ′ − f 0 . ( a ) Show that v ≈ c f beat 2 f 0 , if f beat ≪ f 0 . If f beat = 6670 Hz, what is v (km/h)? ( b ) If the object’s speed is different by Δ v , show that the difference in beat frequency Δ f beat is given by Δ f beat = 2 f 0 Δ v c . If the accuracy of the speed gun is to be 1 km/h, to what accuracy must the beat frequency be measured?
(III) A radar “speed gun” emits microwaves of frequency f 0 = 36.0 GHz. When the gun is pointed at an object moving toward it at speed v , the object senses the microwaves at the Doppler-shifted frequency f . The moving object reflects these microwaves at this same frequency f . The stationary radar apparatus detects these reflected waves at a Doppler-shifted frequency f ′. The gun combines its emitted wave at f 0 and its detected wave at f ′. These waves interfere, creating a beat pattern whose beat frequency is f beat = f ′ − f 0 . ( a ) Show that v ≈ c f beat 2 f 0 , if f beat ≪ f 0 . If f beat = 6670 Hz, what is v (km/h)? ( b ) If the object’s speed is different by Δ v , show that the difference in beat frequency Δ f beat is given by Δ f beat = 2 f 0 Δ v c . If the accuracy of the speed gun is to be 1 km/h, to what accuracy must the beat frequency be measured?
(III) A radar “speed gun” emits microwaves of frequency f0 = 36.0 GHz. When the gun is pointed at an object moving toward it at speed v, the object senses the microwaves at the Doppler-shifted frequency f. The moving object reflects these microwaves at this same frequency f. The stationary radar apparatus detects these reflected waves at a Doppler-shifted frequency f′. The gun combines its emitted wave at f0 and its detected wave at f′. These waves interfere, creating a beat pattern whose beat frequency is fbeat = f′ − f0. (a) Show that
v
≈
c
f
beat
2
f
0
,
if
f
beat
≪
f
0
. If fbeat = 6670 Hz, what is v (km/h)? (b) If the object’s speed is different by Δv, show that the difference in beat frequency Δfbeat is given by
Δ
f
beat
=
2
f
0
Δ
v
c
.
If the accuracy of the speed gun is to be 1 km/h, to what accuracy must the beat frequency be measured?
Suppose a celestial body is moving away from the Earth at a speed of 0.325c. It emits radio waves with a wavelength of 0.765 m. What wavelength would we detect on the Earth?
An out-of-control alien spacecraft is diving into a star at a speed of 1.0 x 108 m/s. At what speed, relative to the spacecraft, is the starlight approaching?
If an object is spherical with a radius of r when viewed at rest, how would its appearance change if it was traveling at relativistic speeds?
Chapter 36 Solutions
Physics For Scientists & Engineers Vol. 3 (chs 36-44) With Modern Physics And Mastering Physics (4th Edition)
Essential University Physics: Volume 2 (3rd Edition)
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