Ncert Exercises & Solutions

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( $100 πt + 0.5 x)$
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(100

πt + 0.5 x)

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]

\cos [(252 + 250) πt]

involving sum and difference of two nearby frequencies 252 and 250, hence, this equation represents beats formation.

(d) As the equation

y = 4 \sin (5 x - t / 2) + 3 \cos (5 x - t / 2)

involves negative sign with x, hence, it represents a travelling wave along +x-direction.

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