Question

$y\left( {x,t} \right) = \dfrac{{0.8}}{{\left[ {{{\left( {4x + 5t} \right)}^2} + 5} \right]}}$, moving pulse. Which is correct?
(A) pulse is moving in +ve x direction
(B) in $2\,\sec$ it will travel a distance of $2.5\,m$
(C) its maximum displacement is $0.16\,m$
(D) it is a symmetric pulse

Answer 1

Hint The solution can be determined by checking every option which is given in the question, when the given condition which is satisfied, then the option is the suitable solution for the question, then the solution can be determined.

Complete step by step answer
1. Pulse is moving in +ve x direction:
In this option, no conditions are given. It gives only the statement by using this statement there is no calculation done in the equation which is given in the question. So, this option will not be the solution for the given question.

2. In $2\,\sec$ it will travel a distance of $2.5\,m$:
In this option, there is only the time value, there will not be the $x$ value. If both the $x$ and $t$ values are given, then the $y$ value can be determined by substituting in the equation which is given in the question. So, this option will not be the solution for the given question.

3. Its maximum displacement is $0.16\,m$:
The maximum displacement is the maximum value of the $y$ in the terms of $x$ and $t$. For the maximum displacement, then the $y$ is maximum, then assume that the term $4x + 5t = 0$, then the equation which is given in the question is written as,
$y\left( {x,t} \right) = \dfrac{{0.8}}{{\left[ {0 + 5} \right]}}$
By adding the terms in the above equation, then the above equation is written as,
$y\left( {x,t} \right) = \dfrac{{0.8}}{5}$
By dividing the terms in the above equation, then the above equation is written as,
$y\left( {x,t} \right) = 0.16\,m$

Hence, the option (C) is the correct answer.

Note For the maximum displacement value, so the $y$ is maximum, then the term which is inversely proportional to the $y$ is almost equal to minimum so we assumed that the term $\left( {4x + 5t} \right)$ is equal to zero. Then the solution can be determined.