Question
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a traveling wave, (ii) a stationary wave or (iii) none at all:
(a) y = 2 cos (3x) sin (10t)
(b) `y = 2sqrt(x- vt)`
(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)
(d) y = cos x sin t + cos 2x sin 2t
Solution 1
(a) The given equation represents a stationary wave because the harmonic terms kxand ωt appear separately in the equation.
(b) The given equation does not contain any harmonic term. Therefore, it does not represent either a travelling wave or a stationary wave.
(c) The given equation represents a travelling wave as the harmonic terms kx and ωtare in the combination of kx – ωt.
(d) The given equation represents a stationary wave because the harmonic terms kxand ωt appear separately in the equation. This equation actually represents the superposition of two stationary waves.
Solution 2
(a) It represents a stationary wave.
(b) It does not represent either a travelling wave or a stationary wave.
(c) It is a representation for the travelling wave.
(d) It is a superposition of two stationary wave.
