If `f_(0)` and `f_(f)` represent the carrier wave frequencies for amplitude and frequency modulations respectively, then

Options

A. `f_(0)gtf_(f)`
B. `f_(0)ltf_(f)`
C. `f_(0)=f_(f)`
D. `f_(0)nef_(f)`

Answer

To solve the question regarding the relationship between the carrier wave frequencies for amplitude modulation (AM) and frequency modulation (FM), we can follow these steps:

### Step-by-Step Solution

1. **Understanding Amplitude Modulation (AM)**:
- In amplitude modulation, the amplitude of the carrier wave is varied in accordance with the information signal. The frequency of the carrier wave remains constant.

2. **Understanding Frequency Modulation (FM)**:
- In frequency modulation, the frequency of the carrier wave is varied according to the information signal, while the amplitude remains constant.

3. **Defining the Frequencies**:
- Let \( f_0 \) represent the carrier frequency for amplitude modulation.
- Let \( f_f \) represent the carrier frequency for frequency modulation.

4. **Comparing the Two**:
- In general, frequency modulation tends to have a wider bandwidth compared to amplitude modulation. This is because frequency modulation can encode more information by varying the frequency over a range.
- Therefore, it is commonly accepted that the frequency used in frequency modulation is greater than that used in amplitude modulation.

5. **Establishing the Relationship**:
- From the above understanding, we can conclude that:
\[ f_0 < f_f \]
- This indicates that the carrier frequency for frequency modulation (\( f_f \)) is greater than that for amplitude modulation (\( f_0 \)).

6. **Selecting the Correct Option**:
- Based on the relationship \( f_0 < f_f \), we can look at the provided options to find the one that matches this inequality. The correct option is the one that states that the amplitude modulation frequency is less than the frequency modulation frequency.

### Final Answer
The relationship can be summarized as:
\[ f_0 < f_f \]
Thus, the correct option is **Option B**.