| MadSci Network: Physics |
Greetings:
During the course of my career in microwave and laser physics I have found that understanding the complexities of the phenomena of interference in 1, 2, and 3 or more dimensions is one of the most fascinating and fundamentally important areas in physics and engineering. It aids in understanding antenna beams and patterns, holograms, radio astronomy techniques, image processing, synthetic array antennas and imaging radar, signal processing, earth quakes and mineral exploration, and animal (bats, moths, whales etc.) and human sonar processing all of which exhibit or use the principles of interference in different , yet basically similar ways. However, there are a number of pit falls that the student is likely to fall into when introduced to interference only in text books without seeing changes with time. I find visual demonstrations provide insight that would take many pages of well written text (which I have not yet found).
The simple one dimensional vibrating string provides the best demonstration for answering your questions. Musical instruments and radio frequency transmissions lines can all be modeled with this simple experiment. I use an old 110 volt 60 Hz ac relay coil to vibrate a thin piece of spring steel at 60 Hz (60 vibrations per second). I tie 3 or 4 feet of fishing line to the vibrating spring and then anchor the loose end of the string to a clamp or some other fixture to place the string in tension. By placing the vibrating string in various states of tension, traveling waves and reflected waves can be made to collide head on. Indeed you are right, when waves of similar amplitude and frequency collide head on, constructive and destructive interference occur in order. This phenomena leads to what are called standing waves and they can be observed in stringed musical instruments, in radio frequency transmission lines and in the experiment above. The points of destructive interference are called nodes and the node spacing is produced by the musicians finger work or the strings tension or both.
VIBRATING
PEAK
* * *
***** ***** *****
******** ******* *******
********** ********* *********
********** ********* *********
------------------------------------------STRING
********** ********* *********
********* ********* *********
******* ******* *******
***** ***** *****
* * *
NODE NODE
Thus 2 waves traveling in opposite directions produce a mode pattern that
is fixed along the string. It is difficult to observe or understand how the
standing wave develops; however, the following program in GW BASIC does a
good job of it. The nodes form at distances A,B,C &D in the print out.
The plot line 210 for your PC is computer and Basic software dependent.
It is not easy to see the nodes in the display. To overlay the time plots
to get an accurate picture of the nodes and peaks set T = 300 in Line 10
and M=10 in line 260
I'll try and add a picture here of the program output in JPEG however, this is my first try at incorporating a picture in an answer and it may not work.40 REM STANDING WAVES DEVELOPED FROM INTERFERING WAVES 50 REM X RANGE = 0 TO 280, Y RANGE= 0 TO 191 60 REM M SETS Y SPACING 100 M=10 110 T=0 120 TF=(T-X)/20 130 TR=(T-279+X)/20 140 IF TF<0 THEN EF=0:GOTO 160 150 EF=SIN(TF) 160 IF TR<0 THEN ER=0:GOTO 180 170 ER=SIN(TR) 180 E=9*(EF+ER) 190 Y=M-E 200 IF Y>191 GOTO 220 210 PSET (X,Y):REM USE THE PLOT FOR YOUR TYPE OF BASIC 220 X=X+1 230 IF X<280 GOTO 120 240 T=T+8 250 X=0 260 M=M+10 270 IF M<191 GOTO 120 1000 END
Regards, your Mad Scientist
Adrian Popa
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