show that when reflection takes place from a boundary separating two media and the velocity in the second medium is infinitely large , the amplitude of the reflected wave is equal to the amplitude of the incident wave and there is a phase change of `pi` in the displacement wave.

Explanation

Suppose a progressive wave of amplitudde `a` is travelling with speed `c` from left to right and there is a rigid wall at ` x = 0 `. Then
`y_(1) = a sin omega ( t - (x)/(c ))`
is the equation of the incident wave
Let `a'` be the amplitude of the reflected wave .
Then ` y _(2) = a' sin omega ( t + ( x)/(c ))` is the equation of the reflected wave .
By the principle of the superposition ` y = y_(1) + y_(2)`
or `y = a sin omega ( t - ( x)/( c)) + a' sin omega ( t + (x)/( c))`
Since the wall is rigid , at ` x = 0 , y = 0 , for all t`
`:. 0 = a sin omega t + a' sin omega t = ( a + a') sin omega t`
`because sin omega t != 0 , a + a' = 0 or a = -a'`
The negative sign shows that there is a phase change by `pi` in the displacement wave.