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400 MHz Wave Length Ball


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A few years ago, and if my memory serves me right, when I was looking into getting my HAM license, I came across the subject of converting a frequency wave length into the metric unit wave length by taking the frequency number in MHz and dividing it into 300 to calculate the wave length into metric units.  As I was exercising this morning with this Exercise Ball, I noticed this Ball is 75 centimeters high and for some reason the conversion formula came to mind because it was labeled as a 75 cm Bosu Ball.  So, using the said formula to calculate the wave length height into a frequency this ball would be the wave length of 400 MHz which this frequency is used for Aeronautical Navigation.  I don't think this frequency is for Radar Altimeters because I think radar altimeters operate around 1 or 1.1 Gigs and Marker Beacons are around the 70 MHz range so that leaves DMEs (Distant Measuring Equipment).  Am I correct?

They also had a GMRS sized Exercise Ball along with an UHF T-Band (500 MHz) ball but I elected to use the Aeronautical Navigation because it is a bigger ball.

75cmBall.thumb.jpg.87a88be27d6809b34ee254832d83e98e.jpg

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The formula for converting between wavelength and frequency is very straightforward. 

Frequency is the number of waves in one second. They’re usually expressed in terms of millions per second (MHz) but could also be thought of as millions of waves per second.

C is the speed of light: 300 million meters per second. RF waves travel through vacuum at the speed of light.

The wavelength is the distance between the same point on any two adjacent waves, expressed in the same units as the speed of light (meters). 

Wavelength x Frequency always equals the speed of light. W x F = C

1 meter = 100 cm.

Algebra allows us to rearrange that to solve for anything you want  

For instance: 

W = C/F

So, for example, you have a frequency of 150 MHz.  300 million meters per second divided by 150 million waves per second equals 2 meters per wave.  In other words 150 MHz is a 2 meter wavelength.

Or find the wavelength for GMRS: 

300 million meters per second divided by 462 million waves per second ≈ 0.65 meters or 65 centimeters wavelength.

Or, given the wavelength, calculate the frequency:

F = C/W

So given 70 cm (0.70 m) the frequency in MHz would be 300/0.70 = 428.5

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1 hour ago, nokones said:

So, with that being said, my memory did serve me right, 75 cm is 400 MHz. Well, not too shabby for an old guy with some memory left in the gray cells.

Exactly!  And wavelength and frequency are inversely related:

1 meter is 300 MHz 

2 meters is 150 MHz 

6 meters is 50 MHz (6 x wavelength-> 1/6 x frequency).

Of course there’s some rounding. The allocated “2 meter band” is just slightly lower in frequency.   

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