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for the wave described in exercise 15 8 plot the...

Question:
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?

Answer:

Given, y(x, t) =3 sin (36t +0.018x + π/4) . . . . . . . . . . . ( 1 )

For x= 0, the equation becomes :

y( 0, t ) =3 sin ( 36t +0 + π/4 ) . . . . . . . . . . . ( 2 )

Also, ω = 2 π/t = 36 rad/s^-1

therefore t = π/18 secs.

Plotting the displacement (y) vs. (t) graphs using different values of t listed below:

t (s)	0	T/8	2T/8	3T/8	4T/8	5T/8	6T/8	7T/8
y (cm)	3√2 / 2	3	3√2 / 2	0	-3√2 / 2	-3	-3√2 / 2	0

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:

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Question:
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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Question: 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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Question:
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?