A Doppler weather radar station broadcasts a pulse of radio waves at frequency 2.85 GHz. From a relatively small batch of raindrops at bearing 38.6° east of north, the station receives a reflected pulse after 180 µs with a frequency shifted upward by 254 Hz. From a similar batch of raindrops at bearing 39.6° east of north, the station receives a reflected pulse after the same time delay, with a frequency shifted downward by 254 Hz. These pulses have the highest and lowest frequencies the station receives, (a) Calculate the radial velocity components of both batches of raindrops. (b) Assume that these raindrops are swirling in a uniformly rotating vortex. Find the angular speed of their rotation.
(a)
The radial velocity components of both batches of raindrops.
Answer to Problem 39.69AP
The radial velocity component of first batch of raindrops is
Explanation of Solution
Given info: The frequency of radio waves is
Write the equation of frequency of radio waves received.
Here,
Write the equation of frequency of radio waves received for another upward shift.
Here,
Substitute
The frequency of radio waves received for upward shift is,
Here,
Substitute
Thus, the value of
Substitute
Thus, the radial velocity of the radio waves with the upward shift is
The frequency of radio waves received for downward shift is,
Here,
Substitute
Thus, the value of
Substitute
The radial velocity of the radio waves with the downward shift is
Conclusion:
Therefore, the radial velocity component of first batch of raindrops is
(b)
The angular speed of the rotation.
Answer to Problem 39.69AP
The angular speed of the rotation is
Explanation of Solution
Given info: The frequency of radio waves is
Write the equation of angular speed of the vortex.
Here,
Write the equation for radius of vortex.
Here,
The radio waves travels towards the rain and comes back.
Write the equation for one way distance covered by the rain.
Here,
Substitute
Substitute
Substitute
Conclusion:
Therefore, the angular speed of the rotation is
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Chapter 39 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
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