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Waves — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWaves5 Marks
Question
For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4cm. 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

All the waves have different phases.

The given transverse harmonic wave is:

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

For x = 0, the equation reduces to:

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

Also,

$\omega=\frac{2\pi}{\text{t}}=36\text{ rad/s}^{-1}$

$\therefore\ \text{t}=\frac{\pi}{18}\text{s}$

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

t (s)

 0

 T/8

 2T/7

 3T/8

 4T/8

 5T/8

 6T/8

 7T/8
y (cm)

 $\frac{3}{\sqrt{2}}$

 3

 $\frac{3}{\sqrt{2}}$

 0

 $-\frac{3}{\sqrt{2}}$

 –3

 $-\frac{3}{\sqrt{2}}$

 0

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