Question 9: Waves

Question

A standing wave $y=A \sin \left(\frac{20}{3} \pi x\right) \cos (1000 \pi t)$ is maintained in a taught string, where $y$ and $x$ are in metres. The distance between two successive points oscillating with the amplitude $\frac{A}{2}$ across a node is

Accepted Answer

The distance of a oscillating point from a node is
$$ y=A \sin \left(\frac{20}{3} \pi xight) $$
$$ \begin{aligned} & 	ext { For } y=\frac{A}{2}, \sin \left(\frac{20}{3} \pi xight)=\frac{1}{2} \ & \Rightarrow \quad \frac{20 \pi x}{3}=\frac{\pi}{6} \ & 	herefore \quad x=\frac{1}{40} \mathrm{~m}=\frac{100}{40} \mathrm{~cm}=2.5 \mathrm{~cm} \end{aligned} $$
Ã¢ÂÂ´ Distance between two successive oscillating points is
$$ D=2 x=2 	imes 2.5=5 \mathrm{~cm} $$

Answer

2.5 cm

Answer

25 cm

Answer

5 cm

Answer

10 cm

Waves

A standing wave y=A \sin \left(\frac{20}{3} \pi x\right) \cos (1000 \pi t) is maintained in a taught string, where y and x are in metres. The distance between two successive points oscillating with the amplitude \frac{A}{2} across a node is

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