A radio station has two channels. One is AM at 1020kHz and the other is FM at 89.5MHz. For good results, you will use

Options

A. longer antenna for the AM channel and shorter for the FM
B. shorter antenna for the AM channel and longer for the FM
C. same antenna length will work for both
D. information given is not enough to say which one to use for which

Answer

To determine which channel (AM or FM) will yield better results in terms of transmission and reception, we can analyze the frequencies and their corresponding wavelengths.

### Step-by-Step Solution:

1. **Identify the Frequencies:**
- AM frequency: 1020 kHz (which is 1.020 MHz)
- FM frequency: 89.5 MHz

2. **Understanding the Relationship Between Frequency and Wavelength:**
- The wavelength (λ) is inversely proportional to frequency (ν). This relationship can be expressed as:
\[ \lambda = \frac{c}{\nu} \]
where \(c\) is the speed of light (approximately \(3 \times 10^8\) m/s).

3. **Calculate Wavelengths:**
- For AM:
\[ \lambda_{AM} = \frac{3 \times 10^8 \text{ m/s}}{1.020 \times 10^6 \text{ Hz}} \approx 294.12 \text{ meters} \]
- For FM:
\[ \lambda_{FM} = \frac{3 \times 10^8 \text{ m/s}}{89.5 \times 10^6 \text{ Hz}} \approx 3.35 \text{ meters} \]

4. **Determine Antenna Lengths:**
- The length of the antenna for efficient transmission and reception is typically one-fourth of the wavelength.
- Length of AM antenna:
\[ L_{AM} = \frac{\lambda_{AM}}{4} = \frac{294.12 \text{ m}}{4} \approx 73.53 \text{ meters} \]
- Length of FM antenna:
\[ L_{FM} = \frac{\lambda_{FM}}{4} = \frac{3.35 \text{ m}}{4} \approx 0.84 \text{ meters} \]

5. **Comparison of Antenna Lengths:**
- Since \(L_{AM} \approx 73.53 \text{ m}\) is greater than \(L_{FM} \approx 0.84 \text{ m}\), we conclude that:
- A longer antenna is required for AM transmission and reception.
- A shorter antenna is sufficient for FM transmission and reception.

6. **Conclusion:**
- For good results, you will use a longer antenna for the AM channel and a shorter antenna for the FM channel.

### Final Answer:
You will use a longer antenna for the AM channel (1020 kHz) and a shorter antenna for the FM channel (89.5 MHz).

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