A radio station broadcasts at 720 kHz. If the radio waves travel at a velocity of `3xx10^(8) ms^(-1)` , calculate the wavelength of the radio waves.

Answer

To solve the problem of finding the wavelength of the radio waves broadcasted by a radio station at 720 kHz, we will use the formula that relates the speed of a wave (V), its frequency (F), and its wavelength (λ):

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency (F) = 720 kHz = 720 × 10^3 Hz
- Velocity (V) = 3 × 10^8 m/s

2. **Use the Wave Equation:**
The relationship between velocity (V), frequency (F), and wavelength (λ) is given by the equation:
\[ V = F \cdot \lambda \]
Rearranging this equation to solve for wavelength (λ):
\[ \lambda = \frac{V}{F} \]

3. **Substitute the Values:**
Now, substitute the known values into the equation:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{720 \times 10^3 \, \text{Hz}} \]

4. **Perform the Calculation:**
- First, calculate the denominator:
\[ 720 \times 10^3 = 720000 \, \text{Hz} \]
- Now, divide the velocity by the frequency:
\[ \lambda = \frac{3 \times 10^8}{720000} \]
- Performing the division:
\[ \lambda = \frac{3 \times 10^8}{7.2 \times 10^5} = \frac{3}{7.2} \times 10^{8 - 5} = \frac{3}{7.2} \times 10^3 \]
- Calculating \(\frac{3}{7.2}\):
\[ \frac{3}{7.2} \approx 0.4167 \]
- Therefore:
\[ \lambda \approx 0.4167 \times 10^3 \, \text{m} = 4.167 \times 10^2 \, \text{m} \]

5. **Final Result:**
The wavelength of the radio waves is approximately:
\[ \lambda \approx 4.17 \times 10^2 \, \text{m} \text{ or } 417 \, \text{m} \]