Question

A wave travelling in positive X-direction with a = 0.2 mt., velocity = 360 mt/sec. and $\lambda= 60 \,mts,$ then correct expression for the wave is:-

• A. $y=0.2 sin\Bigg[2\pi\Bigg(6t+\frac{x}{60}\Bigg)\Bigg]$
• B. $y=0.2 sin\Bigg[\pi\Bigg(6t+\frac{x}{60}\Bigg)\Bigg]$
• C. $y=0.2 sin\Bigg[2\pi\Bigg(6t-\frac{x}{60}\Bigg)\Bigg]$
• D. $y=0.2 sin\Bigg[\pi\Bigg(6t-\frac{x}{60}\Bigg)\Bigg]$

Answer 1

Answer: (C)

$y=0.2 sin\Bigg[2\pi\Bigg(6t-\frac{x}{60}\Bigg)\Bigg]$

Answer 2

The equation of progressive wave travelling in positive $x$-direction is given by
$y=a \sin \frac{2 \pi}{\lambda}(v t-x)$
Here $a=0.2 \,m ,$
$v=360\, m / \sec ,$
$\lambda=60\, m$
$\therefore y=0.2 \sin \frac{2 \pi}{60}(360 \,t-x)$
$=0.2 \sin \left[2 \pi\left(6 t-\frac{x}{60}\right)\right]$