To find the frequency of a radio station broadcasting with a given wavelength, you can use the relationship between the speed of the wave, its wavelength, and its frequency. The formula to calculate the frequency [tex]\( f \)[/tex] is:
[tex]\[ f = \frac{v}{\lambda} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the wave,
- [tex]\( \lambda \)[/tex] is the wavelength.
Given:
- The wavelength [tex]\( \lambda \)[/tex] is 60 meters.
- The velocity [tex]\( v \)[/tex] of the radio wave is [tex]\( 3 \times 10^8 \)[/tex] meters per second.
Now, let's substitute the given values into the formula:
[tex]\[ f = \frac{3 \times 10^8 \, \text{m/s}}{60 \, \text{m}} \][/tex]
[tex]\[ f = 5000000 \, \text{s}^{-1} \][/tex]
or
[tex]\[ f = 5 \times 10^6 \, \text{Hz} \][/tex]
Thus, the frequency of the radio station broadcasting with a wavelength of 60 meters, assuming the velocity of the radio wave is [tex]\( 3 \times 10^8 \, \text{ms}^{-1} \)[/tex], is 5,000,000 Hz or 5 MHz.
