A pulse travelling on a string is represented by the function y - a 3- x - vt 2- a 2-where a -5 mm and v -20 cm s -1 - Sketch the shape of the string at t -0-1 s and 2 s - Take x -0 in the middle of the string-

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 tak ...

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Standard XII

Physics

Wave Speed expression

A pulse trave...

Question

A pulse travelling on a string is represented by the function

$y = \frac{a^{3}}{(x - v t)^{2} + a^{2}},$

where a = 5 mm and $v = 20 c m s^{- 1}$ . Sketch the shape of the string at t = 0, 1s and 2s. Take x = 0 in the middle of the string.

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Solution

The pulse is given by,

$y = [\frac{(a)^{3}}{[(x - v t)^{2} + a^{2}]}]$

a = 5 mm

= 0.5 cm,

v = 20 cm/s

At t = 0s, $y = \frac{a^{3}}{(x^{2} + a^{2})}$

The graph between y and x can be plotted by taking different values of x.

(left as exercise for the student).

Similarly, at t = 1s,

$y = \frac{a^{3}}{{(x - v)^{2} + a^{2}}}$

and at t = 2s, $y = \frac{a^{3}}{{(x - 2 v)^{2} + a^{2}}}$

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A pulse travelling on a string is represented by the function y=a3(x−vt)2+a2, where a = 5 mm and v=20 cm s−1. Sketch the shape of the string at t = 0, 1s and 2s. Take x = 0 in the middle of the string.

The pulse is given by, y=[(a)3[(x−vt)2+a2]] a = 5 mm = 0.5 cm, v = 20 cm/s At t = 0s,y=a3(x2+a2) The graph between y and x can be plotted by taking different values of x. (left as exercise for the student). Similarly, at t = 1s, y=a3{(x−v)2+a2} and at t = 2s, y=a3{(x−2v)2+a2}

A pulse travelling on a string is represented by the function

$y = \frac{a^{3}}{(x - v t)^{2} + a^{2}},$

where a = 5 mm and $v = 20 c m s^{- 1}$ . Sketch the shape of the string at t = 0, 1s and 2s. Take x = 0 in the middle of the string.