Question

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

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

Answer 1

Answer: (C)

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