RADIO WAVES: Frequency, Wavelength, and Physical Length

Amateur Radio Stations transmits voice, Morse codes, or packets, through radio waves.

Radio Communications

Radio Waves is a small portion of the Electromagnetic Waves spectrum.

Electromagnetic Spectrum [2]

Electromagnetic Waves or EM Waves are waves that are created as a result of vibrations between an electric field and a magnetic field. In other words, EM waves are composed of oscillating magnetic and electric fields. [1]

EM Waves are formed when electric field and magnetic field come into contact, thus its name.

EM Waves can be measure by its amplitude (height) and the wavelength (distance between the highest/lowest points of two consecutive waves)

Vertical Polarized Electromagnetic wave

EM waves travel with a constant velocity of 3.00 x 108 m/s in vacuum or space.

It is possible to calculate the wavelength of an EM wave or a Radio Wave given we know the frequency. Frequency is a number of cycles the waves in one second, cycles per second or Hertz (Hz).

Wavelength formula [3]

Example:

What is the wavelength of 145.0 MHz?

Using the formula above, v = 3.00 x 108 m/s and f = 145,000,000 Hz.

Wavelength is 3.00 x 108 m/s divided by 145,000,000 Hz.

Wavelength is 2.0689655172413793103448275862069 meters or 2 meters.

145 MHz has 2 meters of wavelength. This is why we call the 145 MHz Amateur VHF band as a 2 meter band.

The wavelength calculated above is based when the radio waves is travelling in a vacuum or space. This is the standard/reference measurement.

With enough energy, Radio Waves can travel in any medium – be it air, a solid material or vacuum. When the radio waves travels in a different medium, it travels relatively slower than of in vacuum. The term we use to indicate how much a material slows down the propagation of the radio wave is Velocity Factor, often written as VF.

Velocity factor Formula given the dielectric constant. [3]

Radio waves are intercepted by an antenna and converted it to electrical form into what we commonly called, Radio Frequency (RF) electrical signal. The RF signal is in electrical form and behaves as a wave similar to Radio Waves in space or atmosphere. RF signals can also be measured by its amplitude and wavelength similar to Radio Waves.

The velocity of the RF signal is much slower than that of Radio waves in vacuum. VF is less than 1.0. Because the wave is slower, the wavelength becomes shorter.

A radio wave of 2 meters in space is equivalent to 1.98 meters in a bare copper wire suspended in air, VF=0.99.

Wavelength_InCopperWireInAir= is 0.99 x 3.00 x 108 m/s = 1.98 meters.

Wavelength_Vacuum= is 1.0 x 3.00 x 108 m/s = 2 meters.

In antenna design, to tune in a certain wavelength or frequency, the actual physical conductor is trimmed according to its velocity factor, VF.

Where if we are to design a 145 MHz end-fed dipole antenna using a bare copper wire in air; the resulting actual physical length of the copper antenna is shorter by a factor of 0.99 which is the VF value. This shorter equivalent the wavelength in vacuum is what we called physical length.

Below is a visualization of the wavelength in vacuum and it’s equivalent physical length of the copper wire.

Wavelength vs Physical length

Another example for a common coaxial cable RG-58/U PE (Belden 9201), the VF is 0.66, the coax cable equivalent physical length for 145 MHz is 1.32 meters.

In Summary:

Radio waves is an electromagnetic waves composed of electric and magnetic waves.

Waves can me measured by amplitude and wavelength.

Waves travels in a vacuum at the speed of light 3.00 x 108 m/s. Given enough energy, it can travel through anything but relatively slower than in free space. The propagation delay manifested in a shorter equivalent physical measurement.

The physical length is dependent to its dielectric material. The physical length is used in antenna design, and transmission line calculations.

Reference Tables:

Properties of Coaxial Cable Dielectrics
(c = speed of light in a vacuum)
Dielectric TypeTime Delay
(ns/ft)
Propagation
Velocity
Solid Polyethylene (PE)1.540.659c
Foam Polyethylene (FE)1.270.800c
Foam Polystyrene (FS)1.120.910c
Air Space Polyethylene (ASP)1.15-1.210.840c-0.880c
Solid Teflon (ST)1.460.694c
Air Space Teflon (AST)1.13-1.200.850c – 0.900c
Cable VF and Loss [4]

Suggested Readings:

Reference:

[1] https://economictimes.indiatimes.com/definition/electromagnetic-waves

[2] https://commons.wikimedia.org/wiki/File:Electromagnetic-Spectrum.svg

[3] Electronic Communication Systems, 2nd Edition, Blake

[4] https://febo.com/reference/cable_data.html

[5] Coaxial Cable Specifications

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