Question 294: Oscillations

Question

A simple harmonic progressive wave is represented by $$y=A \sin (100 \pi t+3 x)$$. The distance between two points on the wave at a phase difference of $$\frac{\pi}{3}$$ radian is

Accepted Answer

Equation of the given harmonic progressive wave $$y=A \sin (100 \pi t+3)$$ ...... (i)
General equation of a harmonic wave
$$\mathrm{y}=\mathrm{A} \sin (\mathrm{wt}+\mathrm{kx})$$ ..... (ii)
From equations (i) and (ii), $$\omega=100 \pi, k=3$$
But, $$\mathrm{k}=\frac{2 \pi}{\lambda} \Rightarrow 3=\frac{2 \pi}{\lambda}$$
$$	herefore \quad \lambda=\frac{2 \pi}{3}$$
We also know,
Path difference $$\Delta x=\frac{\lambda}{2 \pi} 	imes$$ Phase difference $$\Delta \phi$$
$$\begin{aligned}
	herefore \quad \Delta x & =\frac{2 \pi}{3 	imes 2 \pi} 	imes \frac{\pi}{3} \quad \ldots .\left(	ext { Given } \Delta \phi=\frac{\pi}{3}ight) \
& =\frac{\pi}{9} \mathrm{~m}
\end{aligned}$$

Answer

$$\frac{\pi}{8} \mathrm{~m}$$

Answer

$$\frac{\pi}{9} \mathrm{~m}$$

Answer

$$\frac{\pi}{6} \mathrm{~m}$$

Answer

$$\frac{\pi}{3} \mathrm{~m}$$

Oscillations

A simple harmonic progressive wave is represented by $y=A \sin (100 \pi t+3 x). The distance between two points on the wave at a phase difference of \frac{\pi}{3}$ radian is

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