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# Plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase ?

Q.15.9 For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for $x = 0$, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase?

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$\\y(x,t)=3.0sin(36t+0.018x+\frac{\pi }{4})$

for x = 0

$\\y(t)=3.0sin(36t+\frac{\pi }{4})$

The time period of oscillation is T

$T=\frac{\pi }{18}\ s$

To make the y versus t graph we tabulate values of y(t) at different values of t as follows

 $t$ $0$ $\frac{T}{8}$ $\frac{T}{4}$ $\frac{3T}{8}$ $\frac{T}{2}$ $\frac{5T}{8}$ $\frac{3T}{4}$ $\frac{7T}{8}$ $T$ $y(t)$ $\frac{3}{\sqrt{2}}$ $3$ $\frac{3}{\sqrt{2}}$ $0$ $\frac{-3}{\sqrt{2}}$ $-3$ $\frac{-3}{\sqrt{2}}$ $0$ $\frac{3}{\sqrt{2}}$

The graph of y versus t is as follows

For other values of x, we will get a similar graph. Its time period and amplitude would remain the same, it just will be shifted by different amounts for different values of x.

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