Calculate the wavelength of radio waves of frequency `10^(9) Hz`. The speed of radio waves is `3 xx 10^(8)"m s"^(-1)`.

Options

A. 60 cm
B. 40 cm
C. 30 cm
D. 10 cm

Explanation

To calculate the wavelength of radio waves with a frequency of \(10^9\) Hz and a speed of \(3 \times 10^8\) m/s, we can follow these steps:

### Step 1: Write down the formula for wave speed
The formula that relates the speed of a wave (V), its frequency (ν), and its wavelength (λ) is given by:
\[ V = ν \times λ \]

### Step 2: Rearrange the formula to find the wavelength
To find the wavelength (λ), we can rearrange the formula:
\[ λ = \frac{V}{ν} \]

### Step 3: Substitute the known values
We know:
- Speed of radio waves (V) = \(3 \times 10^8\) m/s
- Frequency (ν) = \(10^9\) Hz

Substituting these values into the formula gives:
\[ λ = \frac{3 \times 10^8 \text{ m/s}}{10^9 \text{ Hz}} \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ λ = \frac{3 \times 10^8}{10^9} = 3 \times 10^{8 - 9} = 3 \times 10^{-1} \text{ m} \]

### Step 5: Convert meters to centimeters
Since 1 meter = 100 centimeters, we convert the wavelength from meters to centimeters:
\[ λ = 3 \times 10^{-1} \text{ m} \times 100 \text{ cm/m} = 30 \text{ cm} \]

### Final Answer
The wavelength of the radio waves is:
\[ λ = 30 \text{ cm} \]

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