Question

Identify the option that correctly represents given wave function.
$y=2\sqrt{3}\sin \pi (x-2t+\frac{1}{6})$

• A.
• B.
• C. Both of the above graphs are possible
• D. None of the two graphs are possible

Answer 1

The correct option is A

Given,
Wave function $y=2\sqrt{3}\sin \pi (x-2t+\frac{1}{6})$
putting $t=0$ and $x=0$ in above equation,
$y=2\sqrt{3}\sin \frac{\pi }{6}$
$\Rightarrow y=\sqrt{3}\text{m}$
At $t=0$ and $x\ne 0$, from the given wave equation we get
$y=2\sqrt{3}\sin (\pi x+\frac{\pi }{6})$
As $x$ value increases $y\uparrow$ up to $y=2\sqrt{3}\text{m}$, because maximum value of $\sin \theta$ is $1$.
Hence, option $\left(a\right)$ is correct representation of given wave function.