A system proposed by the U. S. Navy for underwater submarine communication, called ELF (for extremely low frequency, operates with a frequency of 76 Hz. What is the wavelength of this radiation in meters? In miles? (I mile=1.61 km) What is the energy in joules of the frequency?

The speed of an electromagnetic radiation through vacuum is equivalent

to the speed of light.

Reasons:

The given parameter are;

The frequency of operation of the ELF = 76 Hz

First Part:

Required:

The wavelength of the radiation

Solution:

The speed of the electromagnetic radiation, v = f·λ

Where:

c = The speed of the radiation = 299,792,458 m/s

f = The frequency of the radiation = 76 Hz

λ = The wavelength of the radiation

Therefore;

The wavelength of the radiation ≈ 3.945 km

Second part;

Energy, E = h·f

Where;

h = Planck's constant = 6.62607004 × 10⁻³⁴ m²·kg/s

Therefore;

E = 6.62607004 × 10⁻³⁴ m²·kg/s × 76 Hz = 5.0358132 × 10⁻³² J

The energy in joules of the frequency 5.0358132 × 10⁻³² J

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Explanation:

Frequency = 76 Hz

Wavelength =?

The parameters are related by;

FREQUENCY OF OSCILLATION x WAVELENGTH = SPEED OF LIGHT

Wavelength = Speed of light / Frequency

Wavelength = 299,792,458 / 76

Wavelength = 3944637.61m

Wavelength = 3944.63761 km

Wavelength = 2450.09 miles (Upon conversion to miles by division by 1.61)

Energy = ?

E = h · f

where h = planks constant

Energy = 6.626 * 10^-34 * 76

Energy = 503.576 * 10^-34

Energy = 5.03576 * 10^-32 J