Wavelength frequency and velocity

Wave-Length, Velocity and Frequency

When you pass your Basic Qualification, one of the first ham bands you will probably use is the 2 metre band. Why are you allowed to use that band? Your Basic Qualification allows you to use any ham band provided that the frequency of the radio signals is 30 MHz or higher and athe 2 metre band falls into this category.
Now you are probably thinking "Wait a minute, first he was talking about metres, then he was talking about MHz. Can't he make up his mind?" The answer is that I can't and luckily it doesn't matter.
Metres and Megahertz are simply two ways to measure radio waves. Radio Amateurs switch back and forth, depending on which which way of measurement is most convenient. It's not hard to do. In fact, many people can do it in their heads once they know how.
Before you can convert back and forth you have to know the basic formula: "distance = velocity * time". You may know this formula already from travelling. For example, if you are in car going 100 km/hr. and you travel for 1 hour then you will have gone 100 km. In two hours you will go 200 km and so on. You take the speed the car is going and multiply it by the number of hours you have travelled to get the distance.

Now examine my animation of a radio wave. It is a pictorial representation of the electrical and magnetic waves as a radio wave moves through space. The electric wave is in blue and the magnetic wave is in green. This wave is said to be vertically polarized because the electric wave is up-and-down.
How fast does a radio wave travel? That depends on what it is going through. To make things simple will will look at a radio wave doing through the vacuum of outer space. Radio waves actually travel a bit slower in air but the difference in speed is fairly small.
How fast is a radio wave moving in a vacuum? It moves the same speed as light. Light is just another type of radio wave. Physicists like to use the term c to denote the speed of light. This is also the speed of radio waves.
So how big is c? That is, how fast does a radio wave move? The answer in general terms is fast. In exact terms the answers is 300,000,000 metres per second.
Is that fast? You bet! Suppose you could send a radio wave all the way around the earth; how far would it go in one second? It would go seven times around the earth and be almost half way around again by the time that one second was gone. I don't know about you, but I can't even get out of my chair and turn on a light in one second, let along go more than seven times around the earth!
Ok, once again, the speed of radio waves in a vacuum is 300,000,000 metres per second. This is the same as 300,000 km per second or 300 Mm per second (ie. 300 mega or million metres per second). We will use these speeds interchangeably depending on what is convienient.
Ok, so how does this relate to wavelength and frequency. By definition, the wavelength of a wave is the distance travelled while the wave goes from zero to its maximum, then to its minimum and finally back to zero. This is one complete cycle. (Some people say one cycle is when a wave goes from one maximum to the next. This gives the same wavelength and frequency, but may be a littler easier to describe and imagine.) The frequency is how many cycles there are in one second.
Since we know the speed of a radio wave, if we know how long it takes to complete one cycle we can figure out the distance travelled, and this gives us the length of the wave or as we Radio Amateurs like to call it, the wavelength.
Now as an example, the frequency of the electricity in your house is 60Hz. Since there are 60 cycles in a second, each cycle can only take 1/60th of a second. As a general rule you can get the elapsed time by "fippping-over" the frequency. The mathematical purists call this "getting the reciprocal", but we won't mention that--whoops, we just did...
Remember "distance = velocity * time". Wavelength is a type of distance, time is the frequency flipped over and the velocity is c. Put this all together and we get: lambda = c/f
So where does lambda come from? It's just a fancy way of writing "wavelength". Don't worry, you'll get used to it!
Now, remember all the different ways we wrote c? All right, here's the deal. If the frequency is measured in Mhz it's easiest to use the speed of light measured in Mm/s. That way the "mega's" cancel and we can work with small numbers.
For example, what is the wavelength of a 30Mhz radio wave. One way to calculate this is to convert to hz and calculate 300,000,000/30,000,000 to get 10 metres. Or we can leave the whole thing in Mm and Mhz and calculate 300/30 to get 10 metres. I don't know about you but I don't like writing zeros when I don't need to.
With a Basic Qualification you are allowed to use any ham band where the frequcncy is higher than 30Mhz. It follows from the above paragraph that you can use any ham band where the wave length is shorter than 10 metres.
So what about the 2 metre band? This band goes from 144Mhz to 149Mhz. In terms of wave length this works out as follows:
300/144 = 2.08 metres
300/149 = 2.01 metres
So now you see why this is called the two meter band.
Another band you can use with a Basic Qualification is the 6 metre band. This band goes from 50Mhz to 54 Mhz. Let's calculate the wavelength of the two ends of the band.
300/50 = 6 metres
300/54 = 5.55 metres
So the wavelengths in this band vary from 5.55 metres to 6 metres.
What about going the other way, from wavelength to frequency? You can use the same technique. Since \lambda= c / f it is also true that f = c / \lambda.
Suppose you have a friend who builds a type of antenna called a half-wave dipole measuring 1.5 metre from end to end. What is the frequency of radio waves this antenna will be best at receiving.
Ok, so you may be saying "Whoa! Hold on here just a cotton-picking minute! What's a half-wave dipole?" Well, I don't know how picking cotton got involved with this but I can explain the other things. A dipole is two wires, typically of equal length which are physically hooked up to form one long line, but the two wires are insulated from each other. A half-wave dipole is one half a wavelength long.
So if your friend's antenna is 1.5 metres long then the wavelength is twice that or 3 metres. Now according to the formula, the frequency is given by 300/3 = 100 Mhz. Chances are your friend wants to listen to FM radio.
One word of caution is in order if you want to use the above formula to calculate the size of antennas. Electricity actually travels a bit slower in wires than radio waves travel in a vacuum. Is the difference much? No, but once you get your Morse code endorcement and start using bands below 30Mhz the difference in antenna lengths is noticeable enough to warrant using a separate formula. A good approximation is to use \lambda = 286 / f.
For a more thorough discussion of antennas, please refer to the section on antennas.
In summary, as an electromagnetic wave (ie. a radio wave or a light wave) goes through a cycle it moves through space. The number of cycles it goes through in one second is called the frequency of the wave. The distance it travels as it goes through one cycle is called the wavelength. The speed of radio- wave is basically the same as the speed of light, ie. VERY FAST. The speed of light is 300 Mm/s or 300,000 km/s or 300,000,000 m/s. The formula to convert between wavelength in metres and frequency in MHz is as follows: f =300/ \lambda or \lambda=300/f Of course if ht frequency is in kHz use 300,000 instead of 300. And if the frequency is in Hz then use 300,000,000 m/s for the speed of light.