Resultant Wave Shape When 2 Semicircles Meet

In summary: I didn't mean that you get a bite taken out of the original wave. I meant that the new resultant wave has a shape where it looks like the exact shape of the bottom semi circle has been bitten off from the top one. Anyways i did look at your links and i do understand those ones. and when i apply that same concept to my example, where there is a positive semicircle and a negative smaller semicircle, i get a wrong shape of a resultant wave. Is it possible for anyone to post me a picture of the resultant wave of my example please??
  • #1
jnimagine
178
0
when two waves, one as a crest, one as a trough meet in the middle, a destructive interference happens right?
then if you have a semicircle on top and a smaller semicircle at the bottom, what would the resultant wave look like? I know that you have to take the height of the smaller semicircle out from the top but then when i do this, i just get a shape where a chunk of the smaller semicircle is bitten out of the bigger semicirle at the top. but it isn't supposed to be like this. I know that just taking the exact shape out of the top applies only when the wave is a rectangle. Can anyone please help me as to what my resultant wave should look like??
 
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  • #2
With the supwer position of waves all one does is to add the displacements of the waves together. For example, two wave crests (for simplicity just consider a single crest) traveling in opposite directions cross each other. One has a positive displacement of +1 (corresponding to a crest) and one has a negative displacement of -1 (corresponding to a trough). When the two coincide they cancel as +1 +(-1)= 0.

Now if the trough only has a displacement of -1/2 then it would still cancel the peak when they coincide but not completely and you'd get a peak with a displacemen of +1+(-1/2) = 1/2.
 
  • #3
I found a few websites to illustrate in case I wasn't clear (which I usually am)

http://www.kettering.edu/~drussell/Demos/superposition/superposition.html

This following one is nice because you can play about with the java applet

http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=35

and there are many many more.
 
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  • #4
Kurdt said:
With the supwer position of waves all one does is to add the displacements of the waves together. For example, two wave crests (for simplicity just consider a single crest) traveling in opposite directions cross each other. One has a positive displacement of +1 (corresponding to a crest) and one has a negative displacement of -1 (corresponding to a trough). When the two coincide they cancel as +1 +(-1)= 0.

Now if the trough only has a displacement of -1/2 then it would still cancel the peak when they coincide but not completely and you'd get a peak with a displacemen of +1+(-1/2) = 1/2.

yes i understand that
but if i do it that way i just get a resultant wave that just has a bite out of the top one... which is wrong...
 
  • #5
jnimagine said:
yes i understand that
but if i do it that way i just get a resultant wave that just has a bite out of the top one... which is wrong...

I don't think you're visualising this properly. When you add the amplitudes together you don't get bites taken out of the peaks or troughs. You get a new amplitude which is that of the resultant wave. Nothing happens to the original wave. Did you have a look at some of the graphics on the links I sent? They can be quite useful to study to get your head round.
 
  • #6
Kurdt said:
I don't think you're visualising this properly. When you add the amplitudes together you don't get bites taken out of the peaks or troughs. You get a new amplitude which is that of the resultant wave. Nothing happens to the original wave. Did you have a look at some of the graphics on the links I sent? They can be quite useful to study to get your head round.

I didn't mean that you get a bite taken out of the original wave. I meant that the new resultant wave has a shape where it looks like the exact shape of the bottom semi circle has been bitten off from the top one. Anyways i did look at your links and i do understand those ones. and when i apply that same concept to my example, where there is a positive semicircle and a negative smaller semicircle, i get a wrong shape of a resultant wave. Is it possible for anyone to post me a picture of the resultant wave of my example please??
 

Related to Resultant Wave Shape When 2 Semicircles Meet

Question 1: What is the resultant wave shape when two semicircles meet?

The resultant wave shape when two semicircles meet is a full circle.

Question 2: How does the amplitude of the resultant wave compare to the individual semicircles?

The amplitude of the resultant wave is equal to the sum of the amplitudes of the individual semicircles.

Question 3: Does the phase of the resultant wave change when two semicircles meet?

Yes, the phase of the resultant wave will be affected by the individual phases of the two semicircles.

Question 4: What happens to the frequency of the resultant wave when two semicircles meet?

The frequency of the resultant wave will be the same as the frequency of the individual semicircles.

Question 5: Can the resultant wave shape be altered by changing the size or position of the individual semicircles?

Yes, the resultant wave shape can be altered by changing the size or position of the individual semicircles. This will affect the amplitude, phase, and frequency of the resultant wave.

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