A wave travelling in the positive $x$-direction having displacement along $y$-direction as $1 \mathrm{~m}$,…

A wave travelling in the positive $x$-direction having displacement along $y$-direction as $1 \mathrm{~m}$, wavelength $2 \pi \mathrm{m}$ and frequency of $\frac{1}{\pi} \mathrm{Hz}$ is represented by
  1. $y=\sin (x-2 t)$
  2. $y=\sin (2 \pi x-2 \pi t)$
  3. $y=\sin (10 \pi x-20 \pi t)$
  4. $y=\sin (2 \pi x+2 \pi t)$

Solution

Given $a=1 \mathrm{~m}$ As, $\begin{aligned} y & =\operatorname{asin}(k x-\omega t) \\ & =\sin \left(\frac{2 \pi}{2 \pi} x-2 \pi \times \frac{1}{\pi} t\right) \\ & =\sin (x-2 t) \end{aligned}$ :

Asked in: NEET 2013 (All India)

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