Question 130: Waves

Question

Displacement of a wave is expressed as $x(t)=5 \cos \left(628 t+\frac{\pi}{2}\right) \mathrm{m}$. The wavelength of the wave when its velocity is $300 \mathrm{~m} / \mathrm{s}$ is :
$$(\pi=3.14)$$

Accepted Answer

$$\begin{aligned}
& \mathrm{x}(\mathrm{t})=5 \cos \left[628 \mathrm{t}+\frac{\pi}{2}ight] \mathrm{m} \
& 	ext { velocity }\left(\mathrm{v}_\omegaight)=300 \mathrm{~m} / \mathrm{s} \
& \mathrm{v}_{\mathrm{w}}=\frac{\omega}{\mathrm{K}} \
& 300=\frac{628}{\mathrm{~K}} \Rightarrow \mathrm{~K}=\frac{628}{300} \
& \frac{2 \pi}{\lambda}=\frac{628}{300} \Rightarrow \lambda=\frac{2 	imes 3.14 	imes 300}{628} \
& \lambda=2 \mathrm{~m}
\end{aligned}$$

Answer

0.33 m

Answer

0.5 m

Answer

3 m

Answer

5 m

Waves

Displacement of a wave is expressed as x(t)=5 \cos \left(628 t+\frac{\pi}{2}\right) \mathrm{m}. The wavelength of the wave when its velocity is 300 \mathrm{~m} / \mathrm{s} is : $(\pi=3.14)

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