The velocity of all radiowaves in free space is `3xx10^(8),//s`, the frequency of a wave of wavelength `150 m` is

Options

A. 20 kHz
B. 2 kHz
C. 2 MHz
D. 1 MHz

Answer

To find the frequency of a radio wave with a given wavelength, we can use the formula:

\[ f = \frac{v}{\lambda} \]

where:
- \( f \) is the frequency,
- \( v \) is the velocity of the wave,
- \( \lambda \) is the wavelength.

### Step 1: Identify the given values
- The velocity of the radio waves in free space \( v = 3 \times 10^8 \, \text{m/s} \).
- The wavelength \( \lambda = 150 \, \text{m} \).

### Step 2: Substitute the values into the formula
Substituting the values into the frequency formula, we have:

\[ f = \frac{3 \times 10^8 \, \text{m/s}}{150 \, \text{m}} \]

### Step 3: Simplify the equation
Now, we can simplify the equation:

\[ f = \frac{3}{150} \times 10^8 \]

### Step 4: Calculate \( \frac{3}{150} \)
Calculating \( \frac{3}{150} \):

\[ \frac{3}{150} = \frac{1}{50} = 0.02 \]

### Step 5: Combine the results
Now substituting back into the frequency equation:

\[ f = 0.02 \times 10^8 \]

### Step 6: Express in scientific notation
To express \( 0.02 \times 10^8 \) in standard scientific notation:

\[ 0.02 = 2 \times 10^{-2} \]
Thus,

\[ f = 2 \times 10^{-2} \times 10^8 = 2 \times 10^{6} \, \text{Hz} \]

### Step 7: Convert to Mega Hertz
Since \( 1 \, \text{MHz} = 10^6 \, \text{Hz} \):

\[ f = 2 \, \text{MHz} \]

### Final Answer
The frequency of the wave is \( 2 \, \text{MHz} \).

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