Calculating Radio Wave Velocity

The velocity of a wave, including a radio wave which is an electromagnetic wave, is related to its frequency and wavelength by a fundamental formula.

The relationship is given by:

$\text{Velocity} = \text{Frequency} \times \text{Wavelength}$

In terms of symbols:

$v = \nu \lambda$

Where:

• $v$ is the velocity of the wave.
• $\nu$ (nu) is the frequency of the wave.
• $\lambda$ (lambda) is the wavelength of the wave.

In this problem, we are given the following values for the radio wave:

• Wavelength ($\lambda$) = 12 m
• Frequency ($\nu$) = $25 \times 10^6$ Hz

Now, we can substitute these values into the formula to calculate the velocity of the radio wave.

Step-by-Step Calculation of Radio Wave Velocity

1. Identify the given values:
   $\lambda = 12 \text{ m}$
   $\nu = 25 \times 10^6 \text{ Hz}$
2. Write down the formula relating velocity, frequency, and wavelength:
   $v = \nu \lambda$
3. Substitute the given values into the formula:
   $v = (25 \times 10^6 \text{ Hz}) \times (12 \text{ m})$
4. Perform the multiplication:
   $v = (25 \times 12) \times 10^6 \text{ m/s}$
   $v = 300 \times 10^6 \text{ m/s}$
5. Express the result in standard scientific notation (optional but often required):
   $300 = 3 \times 10^2$
   So, $v = (3 \times 10^2) \times 10^6 \text{ m/s}$
   $v = 3 \times 10^{2+6} \text{ m/s}$
   $v = 3 \times 10^8 \text{ m/s}$

The calculated velocity of the radio wave is $3 \times 10^8$ m/s. This value is approximately the speed of light in a vacuum, which is expected for electromagnetic waves like radio waves.

Comparing this result with the given options, we find that it matches option 2.