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Give below are some functions of x and t...

Give 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)pit]cos[(252+250pit]` (iv)` y=100cos(100pit+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 `+x` direction
Give reasons for your answers.

A

a travelling wave along-xdirection

B

a stationary wave

C

beats

D

a travelling wave along -xdirection

Text Solution

Verified by Experts

The equation `y=100 cos (100pit+0.5x)` is represting a travelling wave along x-direction
(b) The equation `y=5 cos (4x) sin (20t)` represents a stationary wave because it contains sin, cos term i.e. combination of two progressive waves
(c) AS the equation `y=10 cos [(252-250)pit] . cos [(252+250)pit]` involving sum and difference of two near by frequency 252 and 250 have this eqations represents beats formation
(d) As the equation `y=4sin (5x-t//2)+3cos (5x=t//2)` involves negative sing wiht x, have if represents a travelling wae along x-dierection.
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