If the incident wave amplitude is given by some function y1 ( x, t ) f ( x vt ) what waveform has to be superposed with this one to give zero at position x = 0 at all times?
If the incident wave amplitude is given by some function y1 ( x, t ) f ( x vt ) what waveform has to be superposed with this one to give
zero at position x = 0 at all times? Answer: y1 (0, t ) f ( vt ). To get zero we have to add another waveform y 2 (0, t ) f ( vt ). We want the reflected wave to be moving to the right, so we need y 2 ( x, t ) f ( x vt ).
The net wave is given by y1 ( x, t ) y 2 ( x, t ) f ( x vt ) f ( x vt ) Something different happens if a wave is incident on
a moveable boundary. Something different happens if a wave is incident on a moveable boundary.
The general rule is: Whenever a wave is reflected from a free boundary, it is reflected in phase. Whenever it is
reflected from a fixed boundary, it is reflected 180 degrees out of phase. What would happen if the string on the right had exactly
the same properties as the one on the left? What would happen if the string on the right was thicker and denser than the one on the left?
Consider two different wave media that meet at a boundary. The wave speed in medium #1 is v1 and the wave speed in medium #2 is v2. A wave that originates in medium #1 and strikes medium #2 will generally give rise
to a reflected wave and a transmitted wave. The reflected wave is in phase with the original wave if v2 > v1. The reflected wave is 180 degrees out of phase with the
original wave if v2 < v1. Summary: 1. Two or more waves on the same medium produce a net
wave that is determined by the principle of superposition: The amplitude of the resulting wave is the sum of the amplitudes of the individual waves. 2. The reflected wave from a fixed boundary is 180 degrees
out of phase with the original wave. The reflected wave from a free boundary is in phase with the incident wave. 3. When two wave media share a common boundary, a wave incident on that boundary will generally produce both a
reflected and a transmitted wave. The transmitted wave is always in phase with the incident wave while the reflected one is in phase if v2 > v1, out of phase if v2 < v1.
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