Which of the following functions represent a stationary wave ? Here `a , b` and `c` are constants:

Options

A. `y = a cos (bx) sin ( ct)`
B. `y = a sin (bx) cos ( ct)`
C. `y = a sin (bx + ct)`
D. `y = a sin ( bx + ct ) + a sin ( bx - ct)`

Answer

A, B, D

Explanation

A stationary wave is characterized by a function of type ` y = f(t) g(x)`. Hence , choices `(a)` and `(b)` represent a stationary wave . Choice `(d)` is superposition of two oppositely travelling waves of the same amplitude and same frequency , which gives rise to a stationary wave. Hence choice `(d)` also represents a stationary wave.