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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? - Physics

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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Solution 1

All the waves have different phases.

The given transverse harmonic wave is:

`y (x,t)= 3.0 sin (36t + 0.018x + pi/4)` ...(i)

For x = 0, the equation reduces to:

`y (0,t) = 3.0 sin (36t + pi/4)`

Also, `omega = (2pi)/T = 36 " rad/s"^(-1)`

`:. T = pi/8 s`

Now, plotting y vs. t graphs using the different values of t, as listed in the given table.

t(s) 0 T/8 2T/8 3T/8 4T/8 5T/8 6T/8 7T/8
y(cm) `(3sqrt2)/2` 3 `(3sqrt2)/2` 0 `(-3sqrt2)/2` -3 `(-3sqrt2)/2` 0

For x = 0, x = 2, and x = 4, the phases of the three waves will get changed. This is because amplitude and frequency are invariant for any change in x. The y-t plots of the three waves are shown in the given figure.

Solution 2

The transverse harmonic wave is

`y(x,t) = 3.0 sin (36t + 0.018x + pi/4)`

for x = 0

`y(0,t) = 3 sin(36t + 0 + pi/4) = 3 sin (36t + pi/4)`  ...1

Here `omega = (2pi)/T = 36 => T =(2pi)/36`

To plot a(y) versus (t) graph, different values of y corresponding to the values of t may be tabulated as under (by making use of equation 1)

 

t(s) 0 T/8 2T/8 3T/8 4T/8 5T/8 6T/8 7T/8 T
y(cm) `(3sqrt2)/2` 3 `(3sqrt2)/2` 0 `(-3sqrt2)/2` -3 `(-3sqrt2)/2` 0 `3/sqrt2`

Using the values of t and y (as in the table), a graph is plotted as under The graph obtained is sinusoidal.
Similar graphs are obtained for y x = 2 cm and x = 4 cm. The (incm) oscillatory motion in the travelling wave only differs in respect of phase. Amplitude and frequency of oscillatory motion remains the same in all the cases.

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 11 Physics Textbook
Chapter 15 Waves
Q 9 | Page 387
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