A stationary wave is represented by $\mathrm{y}=10 \sin \frac{\pi \mathrm{x}}{4} \cos 20 \pi \mathrm{t}$…
A stationary wave is represented by $\mathrm{y}=10 \sin \frac{\pi \mathrm{x}}{4} \cos 20 \pi \mathrm{t}$ where ' $\mathrm{x}$ ' and ' $\mathrm{y}$ ' are
expressed in $\mathrm{cm}$ and $^{\prime} t^{\prime}$ in second. Distance between two consecutive nodes is
$4 \mathrm{~cm}$
$1 \mathrm{~cm}$
$8 \mathrm{~cm}$
$2 \mathrm{~cm}$
Solution
The stationary wave is:
$y=10 \sin \left(\frac{\pi x}{4}\right) \cos (20 \pi t)$
Nodes occur where $\sin \left(\frac{\pi x}{4}\right)=0$ :
$\frac{\pi x}{4}=n \pi \quad \Rightarrow \quad x=4 n \mathrm{~cm}$
Distance between consecutive nodes:
$\Delta x=4 \mathrm{~cm}$