Question

The position of a wave (of wavelength $\lambda$ ).
$y(x,t)=A\sin 2\pi \left(\frac{x}{\lambda }-3750t\right)$
is shown at $t=0$, find $x$-coordinate of point $P$ in metres, if the wave speed is $300m/sec$ :

• A. $\frac{27\lambda }{12}$
• B. $\frac{29\lambda }{12}$
• C. $\frac{25\lambda }{12}$
• D. $\frac{31\lambda }{12}$

Answer 1

Answer: (C)

$y(x,t)=A\sin (kx-23562t)$
Compare with $y(x,t)=A\sin (kx-\omega t)$ where $\omega =23562$
Hence $f=\frac{23562}{2\pi }=3750Hz$
$\lambda =\frac{v}{f}=\frac{300}{3750}=0.08$
For $y=A/2$ and $t=0$
$\frac{A}{2}=A\sin kx($ since $k=\frac{2\pi }{\lambda })$ or $x=\lambda /12$
Required distance $=2\lambda +\frac{\lambda }{12}=\frac{25\lambda }{12}$