Calculating Cable Length and Node Distance for Standing Electromagnetic Waves

In summary, the problem involves a standing wave pattern on a transmission cable with a frequency of 7.0 MHz and a velocity of 0.95 times the speed of light in a vacuum. The length of the cable is such that the third harmonic has three nodes, and the question is asking for the length of the cable and the distance between nodes on the 7th harmonic. To solve this problem, one must use the equation velocity = frequency x wavelength and understand the definition of a complete wave. The cable length will be equal to the wavelength, and the distance between nodes on the 7th harmonic will be one seventh of the wavelength.
  • #1
avb203796
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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 teh 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.
 
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  • #2
What is the equation relating the speed of light, its frequency and the wavelength?
 
  • #3
velocity=(frequency)(wavelength)?
 
  • #4
yep! Now you know how many wavelengths are on the wire so you can work out how long it is.
 
  • #5
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.
 
  • #6
1Mhz is 1million Hz. What do you know about the definition of a complete wave?
 
  • #7
Half of the wavelength would be the length of the cable correct?
 
  • #8
The cable should be a whole wavelength. Remember a wavelength is measured crest to crest.
 
  • #9
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?
 

FAQ: Calculating Cable Length and Node Distance for Standing Electromagnetic Waves

1. What is an electromagnetic wave?

An electromagnetic wave is a type of energy that is made up of oscillating electric and magnetic fields. It travels through space at the speed of light and does not require a medium to propagate.

2. What are the properties of electromagnetic waves?

Electromagnetic waves have several properties, including wavelength, frequency, amplitude, and polarization. Wavelength is the distance between two consecutive peaks or troughs of the wave. Frequency is the number of waves that pass a point in one second. Amplitude is the height of the wave, and polarization refers to the direction in which the electric and magnetic fields are oscillating.

3. How are electromagnetic waves produced?

Electromagnetic waves are produced by the acceleration of electric charges. This can occur through various processes, such as the movement of electrons in an antenna or the vibrations of atoms in a heated object.

4. What is the electromagnetic spectrum?

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Each type of electromagnetic wave has a different frequency and wavelength.

5. How are electromagnetic waves used in everyday life?

Electromagnetic waves have a wide range of applications in everyday life. Radio waves are used for communication, microwaves for cooking, infrared waves for remote controls, visible light for vision, and X-rays for medical imaging. They are also used in technologies like GPS, Wi-Fi, and cell phones.

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