A radio signal has a frequency of 10 M Hz. The least length of the antenna required for the trans mission of the signal is

Options

A. `7.5` m
B. 5 m
C. `5.5` m
D. `3.5` m

Answer

To find the least length of the antenna required for the transmission of a radio signal with a frequency of 10 MHz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given frequency**:
The frequency \( f \) of the radio signal is given as 10 MHz.
\[ f = 10 \, \text{MHz} = 10 \times 10^6 \, \text{Hz} = 10^7 \, \text{Hz} \]

2. **Use the relationship between speed of light, frequency, and wavelength**:
The speed of light \( c \) is approximately \( 3 \times 10^8 \, \text{m/s} \). The relationship is given by:
\[ c = f \times \lambda \]
where \( \lambda \) is the wavelength.

3. **Rearrange the formula to find the wavelength**:
We can rearrange the formula to solve for \( \lambda \):
\[ \lambda = \frac{c}{f} \]

4. **Substitute the values into the equation**:
Now we can substitute the values of \( c \) and \( f \):
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{10^7 \, \text{Hz}} = \frac{3 \times 10^8}{10^7} = 30 \, \text{m} \]

5. **Calculate the minimum length of the antenna**:
The minimum length \( L \) of the antenna required for transmission is given by:
\[ L = \frac{\lambda}{4} \]
Substituting the value of \( \lambda \):
\[ L = \frac{30 \, \text{m}}{4} = 7.5 \, \text{m} \]

6. **Conclusion**:
Therefore, the least length of the antenna required for the transmission of the signal is:
\[ \boxed{7.5 \, \text{m}} \]