Sure, let's go through the given problem step-by-step to find the wavelength of the wave.
We start with the given data:
- Frequency of the radio station broadcast [tex]\( F \)[/tex] is [tex]\( 600 \text{ kHz} \)[/tex].
- Speed of light in air [tex]\( v \)[/tex] is [tex]\( 3 \times 10^8 \text{ m/s} \)[/tex].
To find the wavelength, [tex]\( \lambda \)[/tex], we will use the relationship between speed, frequency, and wavelength, which is:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
### Step-by-Step Solution:
1. Convert Frequency to Hertz:
Since the given frequency [tex]\( F \)[/tex] is in kilohertz (kHz), we need to convert it to hertz (Hz) for our calculations.
[tex]\[ 600 \text{ kHz} = 600 \times 10^3 \text{ Hz} \][/tex]
So, [tex]\( f = 600,000 \text{ Hz} \)[/tex].
2. Apply the Formula:
The formula to find the wavelength [tex]\( \lambda \)[/tex] is,
[tex]\[ \lambda = \frac{v}{f} \][/tex]
Plug in the values:
- [tex]\( v = 3 \times 10^8 \text{ m/s} \)[/tex]
- [tex]\( f = 600,000 \text{ Hz} \)[/tex]
[tex]\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{600,000 \text{ Hz}} \][/tex]
3. Calculate the Wavelength:
Perform the division:
[tex]\[ \lambda = \frac{3 \times 10^8}{600,000} \][/tex]
[tex]\[ \lambda = 500 \text{ m} \][/tex]
### Conclusion:
The wavelength of the wave broadcast by the radio station at a frequency of [tex]\( 600 \text{ kHz} \)[/tex] with the speed of light in air being [tex]\( 3 \times 10^8 \text{ m/s} \)[/tex] is [tex]\( 500 \)[/tex] meters.
