For the wave described in Exercise 15.8, plot the displacement (y… - Vidyadip

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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