Resultant Wave Shape When 2 Semicircles Meet

[jnimagine]

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??

 

[Kurdt]

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.

 

[Kurdt]

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.

 

[jnimagine]

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...

 

[Kurdt]

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.

 

[jnimagine]

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??