A local radio station can be tuned in by dialing your radio to a frequency of 99 MHz. Calculate the wavelength (in meters) and (joules) (HINT: MHz means 1x106 Hz)

Answer 1

To calculate the wavelength in meters, we can use

c = λν

c = speed of light = 3x10⁸ m/sec

λ = wavelength = ?

ν = frequency = 99 MHz x 1x10⁶ Hz/MHz = 9.9x10⁷ Hz = 9.9x10⁷ sec^-1

Solving for λ we have...

3x10⁸ m/sec = λ * 9.9x10⁷ sec^-1

λ = 3x10⁸ m/sec / 9.9x10⁷ sec^-1

λ = 3.03 m

One cannot calculate the wavelength in joules, as joules is a unit of energy. Perhaps the question meant to also calculate the energy of the radio waves in joules. This requires use of...

E = hc / λ

E = energy in joules = ?

h = Planks constant = 6.626x10^-34 Jsec

c = speed of light = 3x10⁸ m/sec

λ = wavelength in meters = 3.03 m

Solving for E we have...

E = (6.626x10^-34 Jsec)(3x10⁸ m/sec) / 3.03 m

E = 6.56x10^-26 joules