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)
(iv) y = 100cos($100\mathrm{\pi t}+0.5\mathrm{x}\right)$
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

Hint: Analyse each and every option and compare the given equations to the standard equations.
(a) The equation y= 100cos(100 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)$\mathrm{\pi t}\right]$.$\mathrm{cos}\left[\left(252+250\right)\mathrm{\pi t}\right]$ involving sum and difference of two nearby frequencies 252 and 250, hence, this equation represents beats formation.
(d) As the equation $\mathrm{y}=4\mathrm{sin}\left(5\mathrm{x}-\mathrm{t}/2\right)+3\mathrm{cos}\left(5\mathrm{x}-\mathrm{t}/2\right)$ involves negative sign with x, hence, it represents a travelling wave along +x-direction.