For the wave in plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm.

(i) Give the shapes of these plots.

(ii) With respect to which aspects (amplitude, frequency or phase) does the oscillatory motion in a travelling wave differ from one point to another?

Asked by Pragya Singh | 1 year ago |  121

##### Solution :-

Given,

y(x, t) =3 sin (36t +0.018x + $$\dfrac{π}{4}$$)  . .  . . (1)

For x= 0, the equation becomes :

y( 0, t ) =3 sin ( 36t +0 +$$\dfrac{π}{4}$$ )  . .  . . (2)

Also,

ω = $$\dfrac{2π}{t}$$ = 36 rad/s

=> t = $$\dfrac{π}{18}$$ secs.

Similarly graphs are obtained for x = 0, x = 2 cm, and x = 4 cm. The oscillatory motion in the travelling wave is different from each other only in terms of phase. Amplitude and frequency are invariant for any change in x. The y-t plots of the three waves are shown in the given figure:

Answered by Pragya Singh | 1 year ago

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