Question 441: Waves

Question

The equation of wave is given by $$\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$. If the displacement is $$5 \mathrm{~cm}$$ at $$\mathrm{t}=0$$, then the total phase at $$\mathrm{t}=7.5 \mathrm{~s}$$ will be
$$\left[\sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right]
$$

Accepted Answer

$$\begin{aligned} & \mathrm{y}=10 \sin \left(\frac{2 \pi t}{30}+\alphaight) \ & 	ext { At } \mathrm{t}=0, \mathrm{y}=5 \mathrm{~cm} \quad 	herefore 5=10 \sin \alpha \ & 	herefore \sin \alpha=\frac{1}{2} \quad 	herefore \quad \alpha=\frac{\pi^{\mathrm{c}}}{6} \ & 	ext { At } t=7.5 	ext {, the total phase }\& \phi=\frac{2 \pi 	imes 7.5}{30}+\alpha \ & =\frac{\pi}{2}+\alpha \ & =\frac{\pi}{2}+\frac{\pi}{6}=\frac{2 \pi}{3} \mathrm{rad} \ & \end{aligned}$$

Answer

$$\frac{\pi}{3} \mathrm{rad}$$

Answer

$$\frac{\pi}{2} \mathrm{rad}$$

Answer

$$\frac{2 \pi}{5} \mathrm{rad}$$

Answer

$$\frac{2 \pi}{3} \mathrm{rad}$$

Waves

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