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Waves — Physics STD 11 Science — Question

Gujarat 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?
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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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