Read More
Date: 6-2-2021
1609
Date: 2-12-2020
1588
Date: 5-2-2021
1361
|
The superposition principle
The superposition principle states that, if y1(x, t) and y2(x, t) are any two solutions of the wave equation (1),
..........(1)
then so is any linear combination
y(x, t) = A1y1(x, t) + A2y2(x, t) .......(2)
where A1 and A2 are arbitrary constants. This result follows at once from the linearity of the wave equation (1), i.e. each term in the wave equation is proportional to y or one of its derivatives: it does not contain quadratic or higher-power terms or product terms such as y(∂y/∂x). (Equations of this type are known as linear equations.) We can see this as follows. Multiplying the first of the following equations
.......(3)
by A1 and the second by A2, and adding the resulting equations gives
..........(4)
Since
it follows that the linear superposition y(x, t), Equation (2), is also a solution of the wave equation (1). This result clearly generalises to the superposition of any number of solutions of the wave equation. These can be any solutions: they do not have to be normal modes. However, for reasons that will become clearer in the course of the following discussions we now choose a general superposition of normal modes.
|
|
اكتشاف تأثير صحي مزدوج لتلوث الهواء على البالغين في منتصف العمر
|
|
|
|
|
زهور برية شائعة لتر ميم الأعصاب التالفة
|
|
|
|
العتبة العباسية تقيم ورشة علميّة عن عناصر الهُويّة الثقافيّة لوفدٍ من جامعة ذي قار
|
|
قسم الشؤون الفكرية يقيم ورشة تعريفية حول مشاريعه الرقمية في جامعة المثنى
|
|
العتبة العباسية تدعو للمشاركة في مسابقة القصّة القصيرة الثانية ضمن أسبوع الإمامة الدوليّ الثاني
|
|
المجمع العلمي يحيي ذكرى استشهاد الإمام جعفر الصادق (عليه السلام) في كربلاء
|