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Explain the reflection of wave at rigid support.
Solution
A pulse (wave) moving in $+x$-direction and reflecting wave from fixed support are shown in
figure.
If we suppose that the energy is not absorbed at end, then the shape of the reflected pulse will be
same as incident but the phase will be changed by $180^{\circ}(\pi)$.
The reason behind it is the end is fixed. So that the displacement of pulse should be zero.
Suppose, the incident progressive wave displacement at ' $t$ ' time is $y_{i}(x, t)=a \sin (k x-\omega t)$.
Suppose, the displacement of reflected wave is $y_{r}$
According to superposition principle,
$y(x, t)=y_{i}(x, t)+y_{r}(x, t)$
But $y(x, t)=0$
$(\because$ displacement of fixed end is zero $)$
$\therefore 0=y_{i}(x, t)+y_{r}(x, t)$
$\therefore y_{r}(x, t)=-y_{i}(x, t)$
$\therefore y_{r}(x, t)=-a \sin (k x-\omega t)$
