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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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S Sayak

\\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

 

y versus t graph

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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