Given below are some functions of x and t to represent the displacement of an elastic wave.
(i) y =5cos(4x)sin(20t) 
(ii) y = 4sin(5x- t/2) + 3cos(5x- t/2)
(iii)y = 10cos[(252- 250)πt] cos[(252+250)πt]
(iv) y = 100cos(100πt+0.5x)
State which of these represent
(a) a travelling wave along the -x-direction
(b) a stationary wave
(c) beats
(d) a travelling wave along the +x-direction
Give reasons for your answers.

Hint: Analyse each and every option and compare the given equations to the standard equations.
(a) The equation y= 100cos(100πt+ 0.5x) is representing a  travelling wave along -x-direction.
(b) The equation y = 5cos(4x)sin(20t) represents a stationary wave because it contains sin, cos terms i.e., the combination of two progressive waves.
(c) As the equation y= 10cos[(252-250)πt].cos252+250πt involving sum and difference of two nearby frequencies 252 and 250, hence, this equation represents beats formation.
(d) As the equation y=4sin5x-t/2+3cos5x-t/2 involves negative sign with x, hence, it represents a travelling wave along +x-direction.