A travelling wave pulse is given by. $y = \frac{10}{5 + (x + 2 t)^{2}}$ Here, x and y are in metre and t in second. In which direction and with what velocity is the pulse propagating ? What is the amplitude of pulse?

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Solution

Since we have
$y = \frac{10}{5 + {(x + 2 t)}^{2}}$
compare it with
$y = f (x - v t)$
So, $v e l o c i t y = 2 m / s$
$M o v i n g i n^{'} - x^{'} d i r e c t i o n$
For amplitude ; $\frac{d y}{d t} = 0$
$\frac{d y}{d t} = - (10) {[5 + {(x + 2 t)}^{2}]}^{- 2} (2) (2) (x + 2 t)$
$0 = x + 2 t$
$t = \frac{- x}{2}$
So, $y_{m} = \frac{10}{5 + {[x + (\frac{- x}{2}) (2)]}^{2}} = \frac{10}{5} = 2 A = 2$

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