Why do standing waves occur

If an upward displaced pulse is introduced at the left end of the snakey, it will travel rightward across the snakey until it reaches the fixed end on the right side of the snakey. Upon reaching the fixed end, the single pulse will reflect and undergo inversion. That is, the upward displaced pulse will become a downward displaced pulse. Now suppose that a second upward displaced pulse is introduced into the snakey at the precise moment that the first crest undergoes its fixed end reflection.

If this is done with perfect timing, a rightward moving, upward displaced pulse will meet up with a leftward moving, downward displaced pulse in the exact middle of the snakey. As the two pulses pass through each other, they will undergo destructive interference. Thus, a point of no displacement in the exact middle of the snakey will be produced. The animation below shows several snapshots of the meeting of the two pulses at various stages in their interference.

The individual pulses are drawn in blue and red; the resulting shape of the medium as found by the principle of superposition is shown in green. Note that there is a point on the diagram in the exact middle of the medium that never experiences any displacement from the equilibrium position. An upward displaced pulse introduced at one end will destructively interfere in the exact middle of the snakey with a second upward displaced pulse introduced from the same end if the introduction of the second pulse is performed with perfect timing.

The same rationale could be applied to two downward displaced pulses introduced from the same end. If the second pulse is introduced at precisely the moment that the first pulse is reflecting from the fixed end, then destructive interference will occur in the exact middle of the snakey. The above discussion only explains why two pulses might interfere destructively to produce a point of no displacement in the middle of the snakey. A wave is certainly different than a pulse.

What if there are two waves traveling in the medium? Understanding why two waves introduced into a medium with perfect timing might produce a point of displacement in the middle of the medium is a mere extension of the above discussion. While a pulse is a single disturbance that moves through a medium, a wave is a repeating pattern of crests and troughs.

Thus, a wave can be thought of as an upward displaced pulse crest followed by a downward displaced pulse trough followed by an upward displaced pulse crest followed by a downward displaced pulse trough followed by Since the introduction of a crest is followed by the introduction of a trough, every crest and trough will destructively interfere in such a way that the middle of the medium is a point of no displacement.

Of course, this all demands that the timing is perfect. In the above discussion, perfect timing was achieved if every wave crest was introduced into the snakey at the precise time that the previous wave crest began its reflection at the fixed end. In this situation, there will be one complete wavelength within the snakey moving to the right at every instant in time; this incident wave will meet up with one complete wavelength moving to the left at every instant in time.

Under these conditions, destructive interference always occurs in the middle of the snakey. Either a full crest meets a full trough or a half-crest meets a half-trough or a quarter-crest meets a quarter-trough at this point. The animation below represents several snapshots of two waves traveling in opposite directions along the same medium.

The waves are interfering in such a manner that there are points of no displacement produced at the same positions along the medium. These points along the medium are known as nodes and are labeled with an N. There are also points along the medium that vibrate back and forth between points of large positive displacement and points of large negative displacement. These points are known as antinodes and are labeled with an AN.

The two individual waves are drawn in blue and green and the resulting shape of the medium is drawn in black. The animation below depicts two waves moving through a medium in opposite directions. The blue wave is moving to the right and the green wave is moving to the left. As is the case in any situation in which two waves meet while moving along the same medium, interference occurs. The blue wave and the green wave interfere to form a new wave pattern known as the resultant.

The resultant in the animation below is shown in black. The resultant is merely the result of the two individual waves - the blue wave and the green wave - added together in accordance with the principle of superposition. The result of the interference of the two waves above is a new wave pattern known as a standing wave pattern.

Standing waves are produced whenever two waves of identical frequency interfere with one another while traveling opposite directions along the same medium. Standing wave patterns are characterized by certain fixed points along the medium which undergo no displacement. These points of no displacement are called nodes nodes can be remembered as points of no d e s placement. The nodal positions are labeled by an N in the animation above. The nodes are always located at the same location along the medium, giving the entire pattern an appearance of standing still thus the name "standing waves".

A careful inspection of the above animation will reveal that the nodes are the result of the destructive interference of the two interfering waves.