A broadcasting station radiates at a frequency of 710 kHz. What is the wavelength ? Velocity of light `=3 xx 10^8" m/s".`

Answer

To find the wavelength of the broadcasting station that radiates at a frequency of 710 kHz, we can use the formula that relates the speed of a wave (v), its frequency (f), and its wavelength (λ):

\[ v = f \cdot \lambda \]

Where:
- \( v \) is the velocity of the wave (in meters per second),
- \( f \) is the frequency (in hertz),
- \( \lambda \) is the wavelength (in meters).

### Step-by-Step Solution:

**Step 1: Convert the frequency from kilohertz to hertz.**
- The given frequency is 710 kHz.
- To convert kilohertz to hertz, we multiply by 1000:

\[ f = 710 \, \text{kHz} = 710 \times 10^3 \, \text{Hz} = 710000 \, \text{Hz} \]

**Step 2: Use the speed of light.**
- The speed of light is given as \( v = 3 \times 10^8 \, \text{m/s} \).

**Step 3: Rearrange the wave equation to solve for wavelength.**
- We need to find \( \lambda \):

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

**Step 4: Substitute the values into the equation.**
- Substitute \( v \) and \( f \) into the equation:

\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{710000 \, \text{Hz}} \]

**Step 5: Calculate the wavelength.**
- Performing the calculation:

\[ \lambda = \frac{3 \times 10^8}{710000} \approx 422.5 \, \text{m} \]

### Final Answer:
The wavelength is approximately **422.5 meters**.

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