Question

A wave travelling in the +ve $x-$ direction, having displacement along $y-$direction as $1\text{m},$ wavelength $2\pi \text{m}$ and frequency of $\frac{1}{\pi }\text{Hz},$ is represented by-

• A. $y=\sin (2\pi x+2\pi t)$
• B. $y=\sin (x-2t)$
• C. $y=\sin (2\pi x-2\pi t)$
• D. $y=\sin (10\pi x+20\pi t)$

Answer 1

The correct option is B $y=\sin (x-2t)$

Given, $A=1\text{m};\lambda =2\pi \text{m};f=\frac{1}{\pi }\text{Hz}$

$k=\frac{2\pi }{\lambda }=\frac{2\pi }{2\pi }=1\text{and}\omega =2\pi f=\left(2\pi \right)\left(\frac{1}{\pi }\right)=2\text{rad/sec}$

The general expression for a wave travelling in the $+x-$ direction is,

$y=A\sin (kx-\omega t)=\sin (x-2t)$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.