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.

show that when reflection takes place from a boundary separating two m

1.	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.
Answer» Solution :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.