Physics - Sound Wave Question with Solution | TestHub

Here,$y_1=0.05\sin (3\pi t-2x)$

$y_2=0.05\sin (3\pi t+2x)$

According to superposition principle, the resultant displacement is

$y=y_1+y_2$

$=0.05\left[\sin (3\pi t-2x)+\sin (3\pi t+2x)\right]$

$y=0.05\times 2\sin 3\pi t\cos 2x$

$y=\left(0.01\cos 2x\right)\sin 2\pi t=R\sin 3\pi t$

Where$R=0.1 \cos 2 x=$amplitude of the resultant standing wave.

At$x=0.5 \mathrm{m}$

$R=0.1\cos 2x=0.1\cos 2\times 0.5$

$=0.1\cos 1\left(\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\right)=0.1\cos \frac{180°}{\pi }$

$=0.1\cos 57.3°$

$R=0.1\times 0.54\mathrm{m}=0.054\mathrm{m}=5.4\mathrm{c}\mathrm{m}$.