interference , Two or more coherent waves combine to form a resultant wave in which the displacement at any point is the vector sum of the displacements of the individual waves , please explain vector sum of the displacements

Asked by kumarshee | 10th Jul, 2011, 07:31: PM

Expert Answer:

Introduction to vector addition in a plane:

Vectors are physical quantities that are completely described by their magnitude and direction in space.

If there are two vectors   and , their sum   can be calculated by the triangle method as follows:-

Explanation to Vector Addition in a Plane

In the above diagram, we first draw vector , and draw   from the arrow head of . The third side of the triangle is completed by the vector v, which represents the sum of vectors   and .

Thus the sum of two vectors is defined as:

Vector Addition Formula for Vector Addition in a Plane

Force is a vector quantity. Let there be two force vectors   and , acting on the same object. The object is set in motion under the action of the two forces   and . Thus, on the combined action of   and   a third force   is produced and it seems as if the object is set in motion under the effect of this single force . In fact,   is the sum of the two force vectors   and , that is,

 

Now, if the forces   and   are not applied in the same direction, and they are applied with an angle of 30 degrees to each other, the situation will be represented by the following diagram:

In the above diagram, to find the value of , we cannot simply add   and . This is because   and   are not acting in the same direction, and thus their sum will depend on the angle between   and .

Similarly, the resultant of all vector quantities is dependent on the angle between them.

Thus, to add two vectors, we need to take into consideration the angle between the two vectors. Let the angle between two vectors   and   be . The sum of the two vectors,   is given by

 

Answered by  | 11th Jul, 2011, 11:05: AM

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