Question

Which of the following is not the standard from of a sine wave? (Here, symbols have their usual meaning)

• A. $y=A\sin 2\pi (\frac{t}{T}-\frac{x}{\lambda })$
• B. $y=A\sin (vt-kx)$
• C. $y=A\sin \omega (t-\frac{x}{v})$
• D. $y=A\sin k(vt-x)$

Answer 1

The correct option is B $y=A\sin (vt-kx)$

Let take the equation $y=Asin(\omega t-kx)$

We will check each option that can be reduced to the above equation if not, then that option will be the answer of the given question.

Let's check $OptionA:$

$y=Asin2\pi (\frac{t}{T}-\frac{x}{\lambda })$

$Or,y=Asin(\frac{2\pi t}{T}-\frac{2\pi x}{\lambda })$

$Or,y=Asin(\omega t-kx)$

We can see that $y$ is reduced to above equation.

Let's check $OptionB:$

$y=Asin(vt-kx)$

Here, $vt$ has a dimension but $kx$ is dimensionless, so the equation is not possible. There should be $\omega$ in the place of $v$.

Similary, in $OptionC$ and $OptionD$, they can be reduced to the above equation $y=Asin(\omega t-kx)$

So, the correct answer is $OptionB$