Destructive Interference with Different Wave Shapes

[msimard8]

Here is the question


An upright square pulse and an inverted triangular pulse were directed toward each other on a spring, as shown in the illustration. Sketch the appearance of the spring at the instant the two pulses met and completely overlapped. What principle did you use in constructing the shape of the spring for the instant at which the two pulses met? What does this principle state about how waves combine?

i couldn't get the picture in but i think the questions explain it enough

I am assuming the triangle and the square have the same base and height length. I know a triangle is bh\2. Therefore it is smaller than the square. Does this mean the sqaure takes over the triangle like this:

a small square above the string.


What principle is this


thanks

 

[LeonhardEuler]

Here is the question
An upright square pulse and an inverted triangular pulse were directed toward each other on a spring, as shown in the illustration. Sketch the appearance of the spring at the instant the two pulses met and completely overlapped. What principle did you use in constructing the shape of the spring for the instant at which the two pulses met? What does this principle state about how waves combine?
--->
______
| |
| | <----
------------ ----------------\ /----------------
\ /
\/
I am assuming the triangle and the square have the same base and height length. I know a triangle is bh\2. Therefore it is smaller than the square. Does this mean the sqaure takes over the triangle like this:
_____
| |
----------- ---------
What principle is this
thanks

I'm sorry I have difficulty understanding your drawings, but I believe that what is going on is that you have two pulses on a tight spring traveling towards one another. I believe the word you are looking for to describe the method you would use to sketch the solution is "superposition". This principle says that you can simply add the contributions of each pulse at every point to get the total solution. So what you've got to do is add the height of the triangle to that of the square. Since the hiegts have opposite signs they will tend to reduce each other rather than reinforce each other.

 

[quicknote]

for the detailed question! I would like to clarify that destructive interference occurs when two waves with opposite amplitudes meet and cancel each other out. In this case, the square and triangular pulses have opposite shapes, resulting in destructive interference when they meet on the spring.

The principle used in constructing the shape of the spring at the instant the two pulses meet is the principle of superposition. This principle states that when two or more waves meet, the resulting displacement of the medium is equal to the algebraic sum of the individual displacements of each wave.

In this case, the square and triangular pulses will combine to form a new wave with a shape that is a combination of the two original shapes. This is because the individual displacements of each wave will add or subtract from each other, depending on the phase difference between them.

To answer your question about the square "taking over" the triangle, it is important to note that the resulting wave will not be a perfect square or triangle. Instead, it will be a combination of both shapes, with areas of constructive and destructive interference. This means that the amplitude of the resulting wave will be smaller than the individual amplitudes of the square and triangle waves.

In conclusion, the principle of superposition states that when waves meet, their individual displacements will combine to form a new wave with a shape that is a combination of the original waves. This is demonstrated in the destructive interference of the square and triangular pulses on the spring.