Java Applet for Transverse Wave Reflection

1) Java Simulation 

(Please remember to allow running of scripts/ActiveX controls for viewing the applet)

•     AT THE FREE END OF A STRETCHED STRING

Reflection in 3-D spatial-time domain

Applet>Wave Reflection in Spatial-Time Domain(3D Free End)


In this applet, the wave is reflected at 4s at one end of the string (position 100m) and then reflected again at 8s at the other end of the string (position 0m).


Reflection in 2-D spatial domain
Applet>Wave Reflection in Spatial Domain(Free End)


In this applet, the wave is again reflected at one end of the string (position 100m) and then reflected at the other end of the string (position 0m). The monitoring of the wave propagation at any position (position 0m to 100m) can be found at
Applet>Wave Reflection in Time Domain(Free End)

• AT THE FIXED END OF A STRETCHED STRING

Reflection in 2-D spatial domain
 Applet> Wave Reflection in Spatial Domain(Fixed End)


In this applet, the wave is reflected at one end of the wall (position 100m) and then reflected again at the other end of the wall (position 0m). Note that the wave is inverted upon each reflection.  The monitoring of the wave propagation at any position (position 0m to 100m) can be found at
Applet> Wave Reflection in Time Domain(Fixed End)

2) Theory

A transverse wave has particles moving perpendicularly to the direction of travel of the wave.  Each wave particle has the same amplitude and frequency.  Examples of transverse waves are waves on plucked strings, water waves and electromagnetic waves. 


When a transverse wave travels down a stretched string and reaches the end of the string, the entire wave or part of it will be reflected. The reflected wave may be inverted, depending whether the end of the string is free to move or the string is fixed at the end. 

•  Reflection At The Free End 

Figure 1  Reflection of a transverse wave at the free end of a stretched string

The reflection of a transverse wave at the free end of a stretched string is shown in Figure 1. The ends of the string are attached to light rings which are free to slide without friction along the rods. When the wave arrives at the free end, it exerts a force on the element of string there.  This element is accelerated and its motion carries it past the equilibrium points; it "overshoots" and exerts a reaction force on the string.  This generates a reflected wave as shown in Figure 1d and Figure 1e.  It can be seen that  the reflected wave is not inverted compared to the incident wave.  Hence, at the free end, a transverse wave is reflected without a phase change.

A Java simulation in the 3-D spatial-time domain of wave reflection at the free end can be found at this link> Wave Reflection in Spatial-Time Domain(3D Free End). In this applet, the wave is reflected at 4s at one end of the string (position 100m) and then reflected again at 8s at the other end of the string (position 0m).  

A more familiar 2-D spatial domain representation can be found at this link> Wave Reflection in Spatial Domain(Free End). In this applet, the wave is again reflected at one end of the string (position 100m) and then reflected at the other end of the string (position 0m). The monitoring of the wave propagation at any position (position 0m to 100m) can be found at this link> Wave Reflection in Time Domain(Free End). 

•  Reflection At The Fixed End 

  

Figure 2  Reflection of a transverse wave at the fixed end of a stretched string

The reflection of a transverse wave at the fixed end of a stretched string is shown in Figure 2. When the wave reaches the end of the string that is fixed at the wall, the string exerts an upward force on the rigid wall. By Newton's third law, the wall exerts an equal but opposite reaction force on the string. This reaction force causes the wave to invert upon reflection as shown in Figure 2d and Figure 2e.  Hence, at the fixed end, a transverse wave is reflected with a phase change of 180⁰.

A Java simulation in the 2-D spatial domain of wave reflection at the fixed end can be found at this link> Wave Reflection in Spatial Domain(Fixed End). In this applet, the wave is reflected at one end of the wall (position 100m) and then reflected again at the other end of the wall (position 0m).  Note that the wave is inverted upon each reflection. The monitoring of the wave propagation at any position (position 0m to 100m) can be found at this link> Wave Reflection in Time Domain(Fixed End).