Final Answer:
The approximate wavelength of an X Band Radar operating on a frequency of approximately 9500 MHz is about 31.58 centimeters.
Step-by-step explanation:
To find the wavelength of an X Band Radar operating at a certain frequency, we need to use the basic wave equation that relates the speed of light (c), frequency (f), and wavelength (λ).
The speed of light is approximately \( c = 3 \times 10^8 \) meters per second (m/s).
The wave equation is:
\[ c = f \times \lambda \]
Where:
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s).
- \( f \) is the frequency of the wave.
- \( \lambda \) is the wavelength of the wave.
We are given that the radar operates at a frequency of 9500 MHz. MHz stands for megahertz, which is equal to \( 10^6 \) hertz, so we need to convert the frequency from MHz to Hz:
\[ f = 9500 \, \text{MHz} = 9500 \times 10^6 \, \text{Hz} \]
Now we can use the wave equation to solve for the wavelength (λ):
\[ \lambda = \frac{c}{f} \]
Substituting the values we have:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{9500 \times 10^6 \, \text{Hz}} \]
\[ \lambda = \frac{3 \times 10^8}{9500 \times 10^6} \, \text{m} \]
\[ \lambda = \frac{3}{9500} \times 10^2 \, \text{m} \]
\[ \lambda \approx \frac{3}{9.5} \times 10^2 \, \text{m} \]
\[ \lambda \approx 0.3158 \times 10^2 \, \text{m} \]
\[ \lambda \approx 31.58 \, \text{cm} \]
So the approximate wavelength of an X Band Radar operating on a frequency of approximately 9500 MHz is about 31.58 centimeters.