Interference between non-sinusoidal waves

[ArleighBurke]

Hello! I am a 17 year old boy from Italy.
I have a question about interference between non-sinusoidal waves, especially between waves with one crest but without trough (just like the pulse that travels down a rope resting on the ground). I can't really understand what would be the pattern of interference between such type of waves. Can you help me ?
Thank you very much!

 

[Doc Al]

Welcome to PF!

Just like with any other waves, the interference of two pulses can be determined by adding their amplitudes at any given time. If the two pulses are identical (and symmetrical), but travel in opposite directions, there will be a moment when they exactly constructively interfere and thus have double the amplitude. If they are opposite in sign, they will destructively interfere.

Here are two sites that explain this in detail. (The second site gives an animation.)
http://www.physicsclassroom.com/Class/waves/u10l3c.html
http://www.cord.edu/dept/physics/p128/lecture99_33.html

 

[ArleighBurke]

Interference

Thank you for your kind answer! I know that two sinusoidal wave sources should interfere each other creating both constructive and destructive interference. But 2 non-sinusoidal pulse (wave with only crest and no trough in this case) sources should create only constructive interference and then it would bring to creation of energy which is obviously impossible. where is my mistake ?
Thank you and sorry for my bad english
goodbye

 

[Doc Al]

Can you tell me why you think constructive interference implies creation of energy?

 

[ArleighBurke]

Constructive Interference

Hello!
Well I think that a total constructive interference between two wave should double the amplitude but since intensity is proportional to the square of the amplitude a doubled amplitude wave should have quadruplicated intensity. If we speak about sinusoidal wave interference we have both total constructive interference and total destructive one so that we have both doubled amplitude waves (4 times original intensity) and "flat" "destructed" wave (o intensity) and then total energy remains constant. But with 2 pulse waves I think we could have only costructive interference so that resultant amplitude waves would be >(or equal) 2 and < (or equal) 4 but never 0 amplitude!
Thank you
ciao

 

[Crosson]

If we speak about sinusoidal wave interference we have both total constructive interference and total destructive one so that we have both doubled amplitude waves (4 times original intensity) and "flat" "destructed" wave (o intensity) and then total energy remains constant.

You seem to be suggesting that part of the wave constructs and part of the wave destructs in some way that is peculiar to the sinusoidal waveform.

In the case of two sinusoidal waves, they can interfere either totally constructively OR totally destructively but never both at once.

 

[ArleighBurke]

In the case of two sinusoidal waves, they can interfere either totally constructively OR totally destructively but never both at once.

Hello. Yes I know, I meant that when we have two sinusoidal wave radial emitters (with same frequency and amplitude) in some region of space we will have totally constructive interference AND in other regions we will have totally destructive interference.

 

[Doc Al]

Well I think that a total constructive interference between two wave should double the amplitude but since intensity is proportional to the square of the amplitude a doubled amplitude wave should have quadruplicated intensity.

Careful here. Consider a string with two positive pulses heading towards the center of the string. Let's assume they are perfectly triangular pulses of exactly the same amplitude. For each pulse, it is reasonable to say that the energy (KE plus PE) is proportional to the amplitude squared. But what happens when they constructively interfere at the center?

At the instant the pulses overlap in the center, superposition tells us that the shape will be that of a triangle with double the amplitude. So, did the energy somehow become four times greater? No! While the PE has increased, the KE of the string has decreased. Note that this double-sized triangle is not a pulse! (A pulse is something that maintains it's shape as it moves, ignoring dispersion and other complications.) While the energy of a pulse is proportional to amplitude squared, this superposition is not a pulse.

 

[ArleighBurke]

Thanke you for the answer. If I am correct two opposing pulses with same amplitude would form a standing wave which would have much less KE and much more PE. But what would happen if the interferring pulses traveled in the same sense ? for example two radial pulse emitters should form doubled amplitude pulses (but will they be pulses?) traveling in the same direction of the former pulses. mmm I am making some mistakes..
goodbye!