Question

An electromagnetic wave has a frequency of 150 MHz. Its wavelength in air is approximately:

• A. 0.5 m
• B. 1 m
• C. 2 m
• D. 4 m

Hint:

A useful shortcut when working with electromagnetic waves:
Wavelength in meters is given by:
\[ \lambda\text{ (m)} \approx \frac{300}{\text{Frequency in MHz}} \]
Substituting the given frequency: $\lambda \approx \frac{300}{150} = 2\text{ m}$.
This formula is highly effective for solving RF and antenna questions.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question belongs to the topic "Electromagnetic Waves."
The goal is to calculate the wavelength ($\lambda$) of an electromagnetic wave in air when its frequency is given as $150\text{ MHz}$.

Step 2: Key Formula or Approach:
The fundamental relation between the speed of a wave ($v$), its frequency ($\nu$), and its wavelength ($\lambda$) is:
\[ v = \nu \lambda \implies \lambda = \frac{v}{\nu} \]
For electromagnetic waves traveling in air or vacuum, the wave speed ($v$) is approximately equal to the speed of light ($c \approx 3 \times 10^8\text{ m/s}$).

Step 3: Detailed Explanation:

• We are given the following values:
Frequency of the electromagnetic wave ($\nu$) = $150\text{ MHz}$
Since $1\text{ MHz} = 10^6\text{ Hz}$, we can convert this to standard units:
\[ \nu = 150 \times 10^6\text{ Hz} = 1.5 \times 10^8\text{ Hz} \]

• The speed of light in air ($c$) is:
\[ c = 3 \times 10^8\text{ m/s} \]

• Now, substitute these values into the wavelength formula:
\[ \lambda = \frac{c}{\nu} = \frac{3 \times 10^8\text{ m/s}}{1.5 \times 10^8\text{ Hz}} \]

• Simplifying the fraction by dividing the terms:
\[ \lambda = \frac{3}{1.5} = 2\text{ m} \]

• This wavelength of $2\text{ m}$ falls within the VHF (Very High Frequency) band of the radio wave spectrum, commonly used for FM radio transmissions and television broadcasting.



Step 4: Final Answer:
The wavelength of the electromagnetic wave in air is approximately $2\text{ m}$, which corresponds to option (C).