Question

Which of the following functions represent a wave?

• A. (x – v t)²
• B. $\ln (x–vt)$
• C. $e^{-{\left(x-vt\right)}^2}$
• D. $\frac{1}{(x+vt)}$

Answer 1

The correct option is C

$e^{-{\left(x-vt\right)}^2}$

Explanation of the correct answer:
Option C

$e^{-{\left(x-vt\right)}^2}$

1. The wave equation, which describes waves or standing wave fields as they appear in classical physics, including mechanical and electromagnetic waves, is a second-order linear partial differential equation.
2. The function cannot be written as the form $f\left(ax\pm b\right)$ .
3. Therefore the term $e^{-{\left(x-vt\right)}^2}$ is finite.
4. Therefore it is the correct option.
5. 

Explanation of the incorrect options

Option A

${(x–vt)}^2$

1. The function can be written as the form $f\left(ax\pm b\right)$ .
2. Therefore the term ${(x–vt)}^2$ is not finite

Option B.

$\ln (x–vt)$

1. The function can be written as the form $f\left(ax\pm b\right)$ .
2. Therefore the term $\ln (x–vt)$ is not finite

Option D

$\frac{1}{(x+vt)}$

1. The function can be written as the form $f\left(ax\pm b\right)$ .
2. Therefore the term $\frac{1}{(x+vt)}$ is not finite

Hence, option C is the correct option.