for 100 km away, how long it takes 3. One type of radar works by sending a pulse out to and object and timing If the radar is tracking a plane the pulse to return after bouncing off of the object. how long does it take from the time the pulse leaves the radar to the time it returns?
for 100 km away, how long it takes 3. One type of radar works by sending a pulse out to and object and timing If the radar is tracking a plane the pulse to return after bouncing off of the object. how long does it take from the time the pulse leaves the radar to the time it returns?
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![### Understanding Radar Technology
#### Problem 3:
**Scenario:**
One type of radar works by sending a pulse out to an object and timing how long it takes for the pulse to return after bouncing off the object. If the radar is tracking a plane 100 km away, how long does it take from the time the pulse leaves the radar to the time it returns?
The calculations for determining the time are as follows:
1. **Basic Formula:**
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
2. **Variables:**
- Distance to the plane (one way): \( 100 \text{ km} = 100,000 \text{ m} \)
- Speed of radar pulses (speed of light): \( 3 \times 10^8 \text{ m/s} \)
- Since the pulse travels to the plane and back, total distance is \( 200,000 \text{ m} \).
3. **Time Calculation:**
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} = \frac{200,000 \text{ m}}{3 \times 10^8 \text{ m/s}} \approx 6.67 \times 10^{-4} \text{ s} \]
#### Problem 4:
**Radar Antenna Characteristics:**
Radar antennae tend to be of comparable size to their wavelength. The radiation used by radar ranges from 300 MHz to 15 GHz.
**Sub-problem a:**
What is the range of wavelengths?
**Calculations:**
1. **Frequency to Wavelength Conversion:**
\[ \lambda = \frac{c}{f} \]
- \( c \) is the speed of light (\( 3 \times 10^8 \text{ m/s} \))
- \( f \) is the frequency
2. **For \( f = 300 \text{ MHz} \) (which is \( 300 \times 10^6 \text{ Hz} \)):**
\[ \lambda_{\text{max}} = \frac{3 \times 10^8 \text{ m/s}}{300 \times 10^6 \text{ Hz}} = 1 \text{ m} \]
3. **For \( f = 15 \text{ GHz} \) (which](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed0c5231-d007-48db-88ad-3cb0011ef002%2Fa17e72e5-d874-4e55-b7a6-bc1c4f3f14bb%2Fo4mvxfg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Radar Technology
#### Problem 3:
**Scenario:**
One type of radar works by sending a pulse out to an object and timing how long it takes for the pulse to return after bouncing off the object. If the radar is tracking a plane 100 km away, how long does it take from the time the pulse leaves the radar to the time it returns?
The calculations for determining the time are as follows:
1. **Basic Formula:**
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
2. **Variables:**
- Distance to the plane (one way): \( 100 \text{ km} = 100,000 \text{ m} \)
- Speed of radar pulses (speed of light): \( 3 \times 10^8 \text{ m/s} \)
- Since the pulse travels to the plane and back, total distance is \( 200,000 \text{ m} \).
3. **Time Calculation:**
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} = \frac{200,000 \text{ m}}{3 \times 10^8 \text{ m/s}} \approx 6.67 \times 10^{-4} \text{ s} \]
#### Problem 4:
**Radar Antenna Characteristics:**
Radar antennae tend to be of comparable size to their wavelength. The radiation used by radar ranges from 300 MHz to 15 GHz.
**Sub-problem a:**
What is the range of wavelengths?
**Calculations:**
1. **Frequency to Wavelength Conversion:**
\[ \lambda = \frac{c}{f} \]
- \( c \) is the speed of light (\( 3 \times 10^8 \text{ m/s} \))
- \( f \) is the frequency
2. **For \( f = 300 \text{ MHz} \) (which is \( 300 \times 10^6 \text{ Hz} \)):**
\[ \lambda_{\text{max}} = \frac{3 \times 10^8 \text{ m/s}}{300 \times 10^6 \text{ Hz}} = 1 \text{ m} \]
3. **For \( f = 15 \text{ GHz} \) (which
![### Understanding Radar and Imaging Wavelengths
#### 4. Radar Technology
Radar antennas tend to be of comparable size to their wavelength. The radiation used by radar ranges from 300 MHz to 15 GHz.
- **a. What is the range of wavelengths?**
#### 5. Imaging with Different Wavelengths
When used for imaging, the wavelength of the radiation needs to be smaller than the object being imaged. To get a pretty good idea of what kind of radiation is needed to image something, assume that the wavelength of the radiation must be the size of the object or smaller. With this in mind:
- How would visible light work well to image protozoa with a length of 10 micrometers?
- What about bacteria (about 1 micrometer)?
- How about a virus (about 0.1 micrometer)?
#### Additional Considerations
Detailed Calculation Considerations:
For sub-point 4:
- **b. If the antenna dimensions are comparable to the wavelength of the radiation used, what will be the approximate size range of antenna used for radar?**
This question prompts the understanding that radar antennas are designed with reference to the wavelength of the electromagnetic waves they emit.
Note: The image also includes handwriting indicating speed of light calculations involving \(3 \times 10^8\) m/s which are relevant for converting frequencies to wavelengths using the formula:
\[ \text{Wavelength} (\lambda) = \frac{c}{\text{Frequency} (f)} \]
where \( c \) is the speed of light.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed0c5231-d007-48db-88ad-3cb0011ef002%2Fa17e72e5-d874-4e55-b7a6-bc1c4f3f14bb%2Fw5kcvug_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Radar and Imaging Wavelengths
#### 4. Radar Technology
Radar antennas tend to be of comparable size to their wavelength. The radiation used by radar ranges from 300 MHz to 15 GHz.
- **a. What is the range of wavelengths?**
#### 5. Imaging with Different Wavelengths
When used for imaging, the wavelength of the radiation needs to be smaller than the object being imaged. To get a pretty good idea of what kind of radiation is needed to image something, assume that the wavelength of the radiation must be the size of the object or smaller. With this in mind:
- How would visible light work well to image protozoa with a length of 10 micrometers?
- What about bacteria (about 1 micrometer)?
- How about a virus (about 0.1 micrometer)?
#### Additional Considerations
Detailed Calculation Considerations:
For sub-point 4:
- **b. If the antenna dimensions are comparable to the wavelength of the radiation used, what will be the approximate size range of antenna used for radar?**
This question prompts the understanding that radar antennas are designed with reference to the wavelength of the electromagnetic waves they emit.
Note: The image also includes handwriting indicating speed of light calculations involving \(3 \times 10^8\) m/s which are relevant for converting frequencies to wavelengths using the formula:
\[ \text{Wavelength} (\lambda) = \frac{c}{\text{Frequency} (f)} \]
where \( c \) is the speed of light.
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