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Home » For the wave, plot the displacement ( ) versus (t) graphs for 0,2 and . (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?
For the wave, y(x, t)=3 \sin (36 t+0.018 x+\pi / 4) plot the displacement ( y ) versus (t) graphs for x= 0,2 and 4 \mathrm{~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?
CBSE | Class 11 | NCERT | Physics | Waves
For the wave, y(x, t)=3 \sin (36 t+0.018 x+\pi / 4) plot the displacement ( y ) versus (t) graphs for x= 0,2 and 4 \mathrm{~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?

Given wave is,

y(x, t)=3 \sin (36 t+0.018 x+\pi / 4)…..(1)

Putting x=0, the equation becomes:

y(0, t)=3 \sin (36 t+0+\pi / 4)…..(2)

Also,

\omega=2 \pi / \mathrm{t}=36 \mathrm{rad} / \mathrm{s}

\Rightarrow t=\pi / 18 secs

The displacement ( y ) vs. (t) graphs using different values of t is,

\begin{array}{|l|l|l|l|l|l|l|l|l|l|} \hline \mathrm{t} & 0 & \mathrm{~T} / 8 & 2 \mathrm{~T} / 8 & 3 \mathrm{~T} / 8 & 4 \mathrm{~T} / 8 & 5 \mathrm{~T} / 8 & 6 \mathrm{~T} / 8 & 7 \mathrm{~T} / 8 & \mathrm{~T} \\ \hline \mathrm{y} & \frac{3}{\sqrt{2}} & 3 & \frac{3}{\sqrt{2}} & 0 & \frac{-3}{\sqrt{2}} & -3 & \frac{-3}{\sqrt{2}} & 0 & \frac{3}{\sqrt{2}} \\ \hline \end{array}

Similarly, graphs are obtained for x=0, x=2, and x=4. 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:

i

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