describe the The Principle of Superposition for Waves

It often happens that two or more waves pass simultaneously through the same
region. When we listen to a concert, for example, sound waves from many instruments
fall simultaneously on our eardrums. The electrons in the antennas of our
radio and television receivers are set in motion by the net effect of many electromagnetic
waves from many different broadcasting centers. The water of a lake or
harbor may be churned up by waves in the wakes of many boats.
Suppose that two waves travel simultaneously along the same stretched
string. Let Yl(X, t) and Y2(X, t) be the displacements that the string would experience
if each wave traveled alone. The displacement of the string when the waves
overlap is then the algebraic sum

 

y'(x, t) = Yl(X, t) + Y2(X, t).

 

This summation of displacements along the string means that
Overlapping waves algebraically add to produce a resultant wave (or net wave).
This is another example of the principle of snperposition, which says that when several
effects occur simultaneously, their net effect is the sum of the individual effects.
Figure 16-11 shows a sequence of snapshots of two pulses traveling in opposite
directions on the same stretched string. When the pulses overlap, the resultant
pulse is their sum. Moreover,

Overlapping waves do not in any way alter the travel of each other.

 

 

 

 

 

,,,,,,A series of snapshots that
show two pulses traveling in opposite
directions along a stretched string. The
superposition principle applies as the
pulses move through each other.