The Physics of Resonance

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Standing Electrical Waves Demonstration

Standing waves commonly occur on antennas and electric transmission lines but are not visible. To visualize them, we need to build a special piece of equipment called a set of Lecher transmission lines and connect it to a radio transmitter. Fortunately, it's not too hard to do. For example, the Lecher lines will be constructed out of two pieces of ordinary copper tubing. The radio transmitter is the most expensive part but a used one can usually be obtained for about $100.

Once the apparatus is finished we will be able to see the standing waves by placing an ordinary florescent tube between the two transmission lines. The tube will glow brightly at antinodes and dimly at nodes.

We will be using the radio transmitter to produce an electric field between the two transmission lines (copper tubes), so let's start by understanding the nature of these electric fields or e-fields.

Electric field strength indicates the force that would exist on a unit of positive charge if it were located at the point where the electric field is measured. If the charged particle is negative the force on it is reversed. Electric fields cause currents to flow and are a very important part of electromagnetic radiation (a fancy way of saying light which includes the types we see as well as those we don't).

E-field strength at a location inside the florescent tube determines if  the electrons in the tube's contents are excited enough to jumper to higher energy state. When they do, they invariably fall back to their normal state and in the process emit a photon of light. This is what makes the tube glow.

E-fields are vectors and can be represented on vector diagrams in which the length of the arrow represents the e-field's magnitude and the arrowhead the direction. Often e-fields are shown using ray diagrams. The arrowheads on the rays point in the field's direction and the spacing between rays represents the magnitude.

We are going to create a fairly complex standing wave on each transmission line (t-line) so that points directly opposite each other will have opposite charges. Since that's a lot to grasp, let's start by visualizing a simpler case in which the top wire is positive and the bottom wire negative (see Figure 1).

From Figure 1 we see that even this case is not so simple. The blue lines represent the e-field emanating from the top t-line which is positively charged. The red lines represent the e-field emanating from the bottom t-line which is negatively charged.

The dashed lines represent the field above a given t-line and the solid lines below. For example, a blue dashed line represents the e-field above the top positively charge t-line. Note that we are assuming that the wires are very long and are ignoring non-linear fields at the ends.

Figure 1. Ray diagram of an E-field Generated by Two Parallel Transmission Lines with Opposite Charges
Notice that the red and blue e-field rays go in the same direction between the two t-lines. In other words they reinforce each other. The red and blue e-field rays go in opposite directions when they are above or below the pair of t-lines. In other words, they tend to reduce e-field strength. Hence, the e-field is mostly confined to the space between the two t-lines. This will be true even when we eventually apply an AC signal to the t-lines.

In order to insure that a point on one t-line is the opposite sign from a point on the other t-line directly opposite, a small transformer will be connected between the radio transmitter and the t-lines. (These are available from Radio Shack for about $3.) The small transformer also helps keep the radio signal from being broadcast by the wiring between the transmitter and t-lines due to impedance mismatch.

Figure 2. Modified E-field Vector Diagram Showing the Standing Waves on a Pair of Transmission Lines.
  Figure 2 shows a snapshot of the standing waves the radio transmitter will create in the t-lines. Note that this is a modified vector diagram. In other words the length of the arrows indicates the magnitude of the e-field. The pattern of standing waves will create places between the t-lines where the e-field is always zero (called nodes) and other locations where the e-field reaches maximum values (called antinodes).

The red and blue areas will tend to flip-flop over time which is why we refer to Figure 2 as a snapshot. In other words. the bulbous looking parts of the standing waves will alternate between positive and negative e-fields. When a florescent tube is placed between the t-lines, it will glow brightly in these areas. It will glow dimly, if at all, where nodes are located.


The distance between nodes is equal to 1/2 the wavelength of the standing wave. The velocity of the wave on the copper tubes will be the speed of light (3.0 x 108 m/s). The relationship between wavelength, wave speed and transmission frequency is as follows:

  v = l f
    v = wave velocity
    l = wavelength
    f = frequency

For example, a transmission frequency of 400 Hz will give a wavelength of 0.86 meters (30 inches). This would give a spacing of 0.43 meters (15 inches) between nodes.

Procedure/Operating Instructions
After building and assembling the equipment (see "building the equipment" below) you will be ready to use it but first read the cautions listed below. In theory, the t-lines will emitted virtually no radio waves to the outside world. In reality some level of radiation is usually emitted. This can interfere with other radio transmissions. By paying attention to the cautions listed below the potential for problems can be minimized.


  1. Radio frequency power can cause burns. It's best to limit radio transmitter power output to no more than 5 watts and avoid holding fingers or other body parts between the transmission lines.
  2. Even when correct assembled and used, the equipment can create noise in nearby radio transmissions. Be sure to follow the assembly instructions. Keep power levels low and transmission times short. Do not allow students to play with the equipment. Listen to the radio's receiver before transmitting a signal to the transmission lines. Do not transmit if someone is using the frequency.

Place a two foot long plastic florescent fixture between the copper tubes (a four foot plastic fixture will also work but is harder to find). The florescent fixture has to be made of plastic since metal may interfere with the e-field. Florescent grow lights can be used and are generally available in plastic fixtures which are about the same size as a bare florescent tube. The florescent light will be your standing wave detector.

Turn on the florescent light and radio transmitter. Press the transmit button on the radio and hold it down. The tube may brighten slightly when the transmitter goes on. Turn the power off to the florescent tube and continue holding down the transmit button on the radio. The florescent tube should continue glowing.

Move the florescent tube lengthwise between the copper tubes until you locate a node. This will appear as a dark spot in the florescent tube. Notice that the node remains stationary with respect to the copper tubes even when the florescent tube is moved.

Generally, the florescent tube must be turned on before applying the radio signal or the tube will not light. However, once material in the tube is ionized it requires less than a watt of power to keep it glowing. The florescent tube can be lighted using only a radio transmitter but it can easily take over twenty watts of power to do so. A typical handheld transmitter will provide 5 watts at most.

Alternative Demonstrations
The same procedure used to light a florescent tube between the Lecher lines can be used to make a florescent tube glow using only a handheld radio. Once again the tube is turned on and the antenna of the radio held next to it. The transmit button on the radio is pressed and the tube's power turned off. The tube will continue to glow in the area around the antenna even after the power is shut off.  When the radio is moved next to the tube the glow moves with it as long as the transmit button is held down.
We have tried this demo with both a cell phone and a wireless phone without success. At this point it's unclear whether the reason is low power, incorrect frequency, or some other problem.

The advantage of using the Lecher line set instead of the handheld radio's antenna is two fold. First, the handheld antenna will usually not be long enough to display multiple nodes. Second, the Lecher wire set is less likely to interfere with outside radio transmissions.

Troubleshooting Guide
If the florescent tube glows brightly and shows no nodes after the power to the tube is turned off then the radio transmitter may be putting out too much power. This is usually an easy problem to solve even if  your transmitter has no adjustment for reducing power. Start by making sure a 6 Db attenuator (see Table 2) is attached to the matching transformer. This will cut signal power by a factor of four. A second attenuator can be used if needed. Attach it in series with the first. If that doesn't work, try lowering the florescent tube below the two copper tubes. This will reduce the strength of the e-field.

If the frequency of the transmitter is too low the wavelength will be too long and the distance between nodes too large to see. If the frequency is too high the anti-nodes will run together and the tube will appear uniformly bright.

Table 4 gives data for the possible frequencies to use with various lengths of copper tubing. Two frequency ranges are suggested based on radio availability. These should be used with either 4 or 8 foot long lengths of copper tubing in order to observe at least two nodes which can be used for measuring wavelength. Make sure that your radio's frequency is in the correct range for the tube length you have used.

If the florescent tube fails to stay lit when the power is removed then check all connections and make sure the radio has a fresh battery if it uses one. To insure your radio is working, try transmitting to a second radio if you have one. . Sometimes it's possible to light the tube by tilting it. This puts a smaller cross section of florescent tube between the copper tubes and sometimes seems to help. Try removing the 6 Db attenuator (see Table 2). If the tube still fails to light then the transmitter power is probably just not high enough.

A four foot florescent tube can be used but it's harder to light. It's also harder to find one with a plastic fixture. Metal fixtures are not a good idea  since they can interfere with the electric field around the copper tubes.


Building the Equipment

First we need to build a short segment of a transmission line as shown in Figure 1. We'll use two pieces of 3/4 inch diameter 8 foot long copper tubing for the transmission lines and spacers built from pine 2x4's. (Note: 2x4's are commonly used in house construction and usually have to be purchased in 8 foot lengths.) Each spacer set will be held together with a single nylon bolt with a wing nut. (The bolt and wing nut are not shown in Figure 1)



Figure 1. Transmission Line Assembly



Cut a 3"x 6" block of wood out of a 2x4 and then drill the 7/8 inch holes for the copper tubing as shown. Note: 3/4 inch is the inside diameter of the copper tubing. The outside diameter is 7/8 inch. Do not drill 3/4 inch hole in the board. Cut the block into two pieces on a table saw as shown. Be sure to do this after the holes are drilled. This make it possible to tighten the wing nut on the nylon bolt so that the spacer holds the tubes firmly in position.

Generally it's a good idea to make three sets of spacers. If you are using a well made drill press it's often a good idea to clamp the blocks together and drill the tube holes simultaneously through all of the blocks. This helps keep them aligned.

Shorten the 10 foot long  3/4 inch copper tube to 8 feet in length. This makes them much more manageable in the classroom.


Figure 2. Spacer dimensions. (Note: the spacer is cut from a pine 2x4 and is 1.5 inches thick.)


Drill holes in the center of two 3/4 inch copper tubing end caps so that a 1/2 inch long  #8 sheet metal screw can be screwed firmly into them. For the moment, however do not put screws in the holes.  Solder the drilled end caps to one end of each piece of the copper tubing. Solder two unmodified tubing caps to the opposite ends of the two 8 foot long tubes. Make sure that you clean all the surfaces to be soldered with steel wool and flux them with rosin. These surfaces must make good electrical contact or the demonstration will not work. The soldering can be done with a propane torch.

Now you can insert the screws. They will be used as connecting terminals. If they are inserted before soldering, the screws can become soldered to the copper.

Assemble the three wooden spacers to the tubes. These can be positioned at any position along the tubes and moved to various locations as needed.

Attach one of the spade connectors on the matching transformer ( RadioShack part number 15-1230) to the end of each copper tube. Screw on the coaxial to BNC adapter and attach one end of the four foot long cable to the adapter and the other to the radio transmitter. The connecting cable must be 50 Ohm coaxial cable or there will be a mismatch of impedances between the radio and the cable. This reduces efficiency by reflecting part of the signal back into the radio.

Do not attempt to connect the radio directly to the copper tubes without using the matching transformer. This will cause a mismatch in impedance between the cable and the copper tubes which turns the connecting cable into a transmitting antenna. This can cause unwanted noise in local radio transmissions. The whole idea behind the Lecher transmission lines is to confine the e-field between the transmission lines. This prevents the transmission of signals to the outside world.

Once all the equipment is assembled you are ready to test it. See above for operating instructions.

Table 1. Materials for Building the Lecher Wire Set
Num. Quantity Price Item Total Comments
2 each $5.60 10 ft long straight pieces of 3/4 inch copper tubing. $11.20 These will be shortened to 8 ft. If you decide to build a 4 ft set of t-lines buy a single 10 ft long piece of tubing. Be sure to check the tubes for straightness.
4 each 0.30 3/4 inch copper tubing end caps 1.20  
1 each 3.00 a 20 inch long piece of pine 2 x 4 (note that the price is for an 8 foot long 2 x 4 board) 3.00 Normally an 8 foot long 2 x 6 is the shortest length which can be purchased. The project will only use 18 inches. Spend a little extra and get the highest quality wood you can find. It will give better results with very little extra cost.
3 each 0.60 1/4 inch dia x 2 inch long nylon bolt with washer and wing nut 1.80 These need to be nylon to eliminate possible interaction with the electric field which will be generated between the two copper tubes.

Pre-Tax Total


Cost is approximate and will vary from location to location.


Table 2. Electrical Materials Required to Operate the Lecher Wire Set

Num Quantity Price Item Total Comments
1 each $4.00 300 Ohm to 75 Ohm Matching Transformer part # 15-1230. (RadioShack) $4.00 This is an essential item which prevents the connecting wire from acting like an antenna.
1 each 1.70 Female BNC to Coaxial Adapter (RadioShack) 1.70  
1 each 3.50 6 Db, TV/VCR Signal Overload Attenuator part number 15-1257A. (RadioShack) 3.50  
1 each 6.00 3 foot long coax RG-58 (BNC to BNC) patch cable. (RadioShack) 6.00 typical coax cables are 75 or 50 ohm impedance. 50 ohm (as specified at left) is needed to connect to handheld radios.
1 each   Handheld radio transmitter , 4-5 watt maximum output. Generally outputs of as little as one watt will work. 100 Used 250 new Usually handheld battery operated units work well.
1 each 8.00 2 Foot Long Single Tube Plastic Florescent Fixture With Tube. (Walmart) 8.00 Grow lights or standard florescent tubes work well. A larger tube will show more nodes but is harder to find with a thin plastic housing
Pre-Tax Total without radio or Lecher Wire Set $23.20 Cost is approximate and will vary from location to location.
Pre-Tax Total with Lecher Wire Set but not radio $40.40 Cost is approximate and will vary from location to location.
Pre-Tax Total Entire system $140 to $290 Depends on radio cost


Table 3. Required Tools

table saw, drill press, soldering gun or propane torch, tubing cutter, misc. hand tools
steel wool for cleaning copper surfaces, small container of rosin flux, rosin core solder

Finding a Radio Transmitter
If you're already a HAM radio operator then this part is easy, however, for everyone else it's going to take some effort. First, a few disclaimers: We have done our best to provide reliable information about options in radios but the FCC does make changes and we may not have interpreted all their rules correctly. We suggest that you check with the FCC ( before you buy a radio to make sure you comply with the applicable rules.

Note that the length of the copper tubing used in the transmission lines is determined by the radio's frequency. The minimum sizes suggested will make it possible to detect at least two nodes with the florescent tube.


Table 4. Radio Transmitter Options

Type Frequency Range (MHz) wavelength (m) 1/4 WL (m) Min. Cu Tubing Lenth (ft) License Restrictions Comments
GMRS 463 to 468 0.7 0.16 4 $75 fee, no test 5 watts max power UHF Business band
MURS 152 to 155 1.9 0.49 8 None 2 Watts max power VHF Business band
HAM 144 to 148 2 0.5 8 HAM   A technician class license is relatively easy to obtain and does not require Morse code.
HAM 420 to 450 0.7 0.17 4 HAM   A technician class license is relatively easy to obtain and does not require Morse code.

Prices vary on GMRS and MURS type handheld radios but expect to pay $150 to $250. Dealers can be found using web search engines such as google. HAM hand held radios in appropriate frequencies are similar in cost. In general, there is no reason to buy a unit with more than 5 watts of output power. Generally about one watt is enough.

You MUST have a radio with a detachable antenna using a BNC connector. Other kinds of connectors can be used but they will require special adapters to connect to the BNC connectors on the cable attaching the radio to the transition lines.

DO NOT BUY family radio service (FRS) handheld systems for use with Lecher lines. These do not have detachable antennas and cannot be connected to the transmission lines. FSR units are low power, low cost units which are commonly sold in places like Walmart and RadioShack.

Handheld radio receivers can often be purchased used for half price or less. The best place to find them is at HAM Fests. These are like flea markets for HAM radio operators. Check here for one in your area. Used radios are also available on e-bay.

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