Question 403: Waves

Question

A stationary wave is represented by
$$\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t})$$
where $$\mathrm{x}$$ and $$\mathrm{y}$$ are in $$\mathrm{cm}$$ and $$\mathrm{t}$$ in second. The distance between two consecutive nodes is

Accepted Answer

$$y=10 \sin \left(\frac{\pi x}{4}ight) \cos (20 \pi t)$$
Comparing with $$\mathrm{y}=2 \mathrm{~A} \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}ight) \sin \left(\frac{2 \pi \mathrm{t}}{\mathrm{T}}ight)$$, we get
$$\begin{aligned}
& \frac{2 \pi \mathrm{x}}{\lambda}=\frac{\pi \mathrm{x}}{\mathrm{T}} \quad 	herefore \frac{2}{\lambda}=\frac{1}{4} \
& 	herefore \lambda=8 \mathrm{~cm}
\end{aligned}$$
$$	herefore$$ The distance between two consecutive nodes
$$=\frac{\lambda}{2}=\frac{8}{2}=4 \mathrm{~cm}$$

Answer

1 cm

Answer

8 cm

Answer

4 cm

Answer

2 cm

Waves

A stationary wave is represented by $\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t}) where \mathrm{x} and \mathrm{y} are in \mathrm{cm} and \mathrm{t}$ in second. The distance between two consecutive nodes is

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