If critical frequency is 20 MHz for ionosphere, calculate the angle of transmission if 30 MHz frequency is transmitted.

Options

A. `cos ^(-1)((2)/(3))`
B. `sin ^(-1)((2)/(3))`
C. `cos ^(-1)((1)/(3))`
D. `sin ^(-1)((1)/(3))`

Answer

To solve the problem of calculating the angle of transmission when a frequency of 30 MHz is transmitted and the critical frequency is 20 MHz, we can follow these steps:

### Step 1: Identify the given values
- Critical frequency, \( f_c = 20 \) MHz
- Maximum frequency transmitted, \( f_{max} = 30 \) MHz

### Step 2: Use the relationship between critical frequency and angle of transmission
The relationship between the critical frequency and the angle of transmission is given by the formula:
\[ f_{max} = \frac{f_c}{\cos \theta} \]
where \( \theta \) is the angle of transmission.

### Step 3: Rearrange the formula to find \( \cos \theta \)
From the formula, we can rearrange it to find \( \cos \theta \):
\[ \cos \theta = \frac{f_c}{f_{max}} \]

### Step 4: Substitute the values into the equation
Now, substituting the given values into the equation:
\[ \cos \theta = \frac{20 \text{ MHz}}{30 \text{ MHz}} \]
This simplifies to:
\[ \cos \theta = \frac{20}{30} = \frac{2}{3} \]

### Step 5: Calculate \( \theta \)
To find the angle \( \theta \), we take the inverse cosine:
\[ \theta = \cos^{-1}\left(\frac{2}{3}\right) \]

### Step 6: Final calculation
Using a calculator or trigonometric tables, we can find:
\[ \theta \approx 48.19^\circ \]

### Conclusion
Thus, the angle of transmission when a frequency of 30 MHz is transmitted is approximately \( 48.19^\circ \).