Question

What is the energy, in joules, of a wave with a frequency of `6.78 * 10^7` Hz? What type of wave is this?

Answer 1

I think it is a FM radio signal with photon energy of around `4.49xx10^-26J`.

Explanation:

Let us check (as an exercise) the wavelength `lambda` of this wave using:
`c=lambda*nu`
where:
`c=3xx10^8m/s` is the sped of light;
`nu=6.78xx10^7Hz` is the frequency.
so you get:
`lambda=(3xx10^8)/(6.78xx10^7)=4.42m` quite a big wavelength!
considering:

I would say that it falls into the FM radio range.

The energy can be calculated from Einstein's Relationship:
`color(red)(E=hnu)`
Where:
`h=6.63xx10^-34Js` is Planck's constant.
So:
`E=6.63xx10^-35*6.78xx10^7=4.49xx10^-26J`