Answer:
Wavelength is 3.08 meters.
Explanation:
It is given that,
Frequency, [tex]f=97.2\ MHz=97.2\times 10^6\ Hz[/tex]
We need to find the wavelength of the carrier wave of a campus radio station. It can be calculated by using following relation as :
[tex]c=f\times \lambda[/tex]
[tex]\lambda=\dfrac{c}{f}[/tex]
[tex]\lambda=\dfrac{3\times 10^8\ m/s}{97.2\times 10^6\ Hz}[/tex]
[tex]\lambda=3.08\ m[/tex]
So, the wavelength of the carrier wave is 3.08 meters. Hence, this is the required solution.
The wavelength of the carrier wave of the campus radio station, broadcasting at the given frequency is 3.086m.
Given the data in the question;
Using the relation between wavelength and frequency:
[tex]v = \frac{c}{\lambda}[/tex]
Where, v is the frequency, c is the speed of light ( 3.8 × 10⁸ m/s ) and λ is the wavelength.
We substitute our values into the equation
[tex]97.2*10^6 s^{-1} = \frac{3*10^8m/s}{\lambda} \\\\\lambda = \frac{3*10^8m/s}{97.2*10^6 s^{-1}}\\\\\lambda = 3.086 m[/tex]
Therefore, the wavelength of the carrier wave of the campus radio station, broadcasting at the given frequency is 3.086m.
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