Subjective Type

A pulse travelling on a string is represented by the function $$y = \dfrac{a^3}{(x - vt)^2 + a^2}$$ Where $$a = 5 mm$$ and $$v = 20 cm /s$$. Sketch the shape of the string at $$t = 0, \ 1 s$$ and $$2 s$$. Take $$x = 0$$ in the middle of the string.

Solution

The pulse is given by , $$y= [(a^3) /\{(x - vt)^2 + a^2\}]$$
$$a = 5 mm = 0.5 cm, v = 20 cm/s$$
At $$t = 0s, y = a^3/(x^2 + a^2)$$
The graph between y and x can be plotted by taking different values f x.
Similarly, at $$t = 1 s , y = a^3/\{(x - v)^2 + a^2\}$$
and at $$t = 2s, \,\, t = a^3/ \{(x - 2v)^2 + a^2\}$$

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