Question

Given below are some functions of x and t to represent the displacement of an elastic wave. 

(a) y = 5cos (4x) sin (20t) 

(b) y = 4 sin (5x − t/2) + 3 cos (5x – t/2)

(c) y = 10 cos [(252 – 250)πt] + cos[(252 + 250)πt)]

(d) y = 100 cos(100πt + 0.5x)

State which of these represent

(a) A travelling wave along-x direction (b) A stationary wave (c) Beats (d) A travelling wave along 4 + x direction. Given reasons for your answers.

Answer 1

(a) Equation y = 100 cos(100πt + 0.5x) represents a travelling wave along x-direction.

(b) Equation y = 5 cos (4x)sin (20t) represents stationary wave, as this is combination of progressive waves (contains sin, cos, terms)

(c) Equation y = 10 cos[(252 − 250)πt] cos[(252 + 250)πt] represent beats formation because this equation involve sum & difference of two nearby frequencies i.e., 252, 250.

(d) Equation y = 4 sin (5x − \(\frac{t}{2}\) ) + 3 cos (5x − \(\frac{t}{2}\) ) represent a travelling wave along +x direction because it involves negative sign with x.