Calculating Cable Length and Node Distance for Standing Electromagnetic Waves

[avb203796]

I have yet another problem that I need help with. An elctromagnetic wave with a frequency of 7.0 MHz forms a standing wave pattern on a transmission cable. The velocity of the wave in the cable is 0.95 of the speed of light in a vacuum. the length of the cable is such that the third harmonic has three nodes along the length of the cable, one at each end, and one in the middle. how long is the cable? what is the distance between the nodes of the 7th harmonic on the cable?

I believe that the speed of light in a vacuum is equal to to 3.0 x 10^8 m/s therefore, the velocity of the wave would be 2.85 x 10^8 right?

But now where do I go from there? I am not sire what my next step should be.

 

[Kurdt]

What is the equation relating the speed of light, its frequency and the wavelength?

 

[avb203796]

velocity=(frequency)(wavelength)?

 

[Kurdt]

yep! Now you know how many wavelengths are on the wire so you can work out how long it is.

 

[avb203796]

Do I need to convert my 7.0 MHz to Hz and if so what is the conversion factor? Also, how do I know how many wavelengths are on a wire? the above formula gives me the wavelength but then I am not sure how many wavelengths are on the wire.

 

[Kurdt]

1Mhz is 1million Hz. What do you know about the definition of a complete wave?

 

[avb203796]

Half of the wavelength would be the length of the cable correct?

 

[Kurdt]

The cable should be a whole wavelength. Remember a wavelength is measured crest to crest.

 

[avb203796]

Ok so then my cable length would be equal to my wavelength and the distance between nodes on the 7th harmonic would be 1/7 of the wavelength?