Explain the reflection of wave at free support.

Explanation

As shown in figure, the string is fastened to a ring which slides without friction on a rod. In this case, when the pulse arrives at the left end, the ring moves up the rod.

As the ring moves, it pulls on the string stretching the string and producing a reflected pulse with the same sign and amplitude as the incident pulse. Thus, in such a reflection, the incident and reflected pulses reinforce each other, creating the maximum displacement at the end of the string, the maximum displacement of the ring is twice the amplitude of either of the pulses. Thus, the reflection is without any additional phase shift.
Here, the reflection takes place without any phase change.
Suppose the progressive wave is,
`y _(1) (x,y) a sin (kx - omega t )`
The reflected wave from open end is:
The reflected wave form open end is,
`y _(r) (x,t) = a sin (kx + omega t )`
If incident wave is moving in +X-direction, then reflected wave would be moving in -X-direction.
Note: If progressive was is moving in + Y-direction then the reflected wave of
`x _(i) (y,t) =a sin (kx - omega t ) is x _(r) (y,t) = - a sin (ky - omega t )`