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 travelling wave, (ii) a stationary wave or (iii) none at all: y = cos x sin t + cos 2x sin 2t.
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question is incomplete. A complete question is -----> 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 travelling wave, (ii) a stationary wave or (iii) none at all:
(a) y = 2 cos (3x) sin (10t)
(b) y = 2√(x - vt)
(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)
(d) y = cos x sin t + cos 2x sin 2t
let's start to check !
(a) y = 2cos(3x)sin(10t)
use formula, 2sinA.cosB = sin(A + B) + sin(A - B)
so, y = sin(10t + 3x) + sin(10t - 3x)
here , it is clear that y = 2cos(3x).sin(10t) is the superposition of same progressive waves which are in opposite directions.
hence, it represents stationary wave.
(b) It doesn’t represent either a travelling wave or a stationery wave. it is just an equation of square root function.
(c) It is a representation for the travelling wave.
(d) It represents the superposition of two stationery waves.
(a) y = 2 cos (3x) sin (10t)
(b) y = 2√(x - vt)
(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)
(d) y = cos x sin t + cos 2x sin 2t
let's start to check !
(a) y = 2cos(3x)sin(10t)
use formula, 2sinA.cosB = sin(A + B) + sin(A - B)
so, y = sin(10t + 3x) + sin(10t - 3x)
here , it is clear that y = 2cos(3x).sin(10t) is the superposition of same progressive waves which are in opposite directions.
hence, it represents stationary wave.
(b) It doesn’t represent either a travelling wave or a stationery wave. it is just an equation of square root function.
(c) It is a representation for the travelling wave.
(d) It represents the superposition of two stationery waves.
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