Question

The oscillations of two points x1 and x2 at x = 0 and x = 1 m respectively are modelled as follows: y1 = 0.3 sin 4πt and y2 = 0.3 sin (4πt +π / 8) Calculate the wavelength and speed of the associated wave.

Answer 1

Answer on Question #65637- Physics Mechanics Relativity

The oscillations of two points $x1$ and $x2$ at $x = 0$ and $x = 1$ m respectively are modelled as follows: $y1 = 0.3 \sin 4\pi t$ and $y2 = 0.3 \sin (4\pi t + \pi / 8)$ . Calculate the wavelength and speed of the associated wave.

Data:

$$y _ {1} = 0. 3 \sin (4 \pi t); x = 0 m$$ $$y _ {1} = 0. 3 \sin \left(4 \pi t + \frac {\pi}{8}\right); x = 1 m$$

Solution:

$$\Delta \varphi = \left(4 \pi t + \frac {\pi}{8}\right) - 4 \pi t = \frac {\pi}{8};$$ $$\frac {\pi}{8} - 1 m$$ $$2 \pi - \lambda m$$ $$\lambda = 16 m;$$ $$w = 2 \pi v = 4 \pi ; \quad v = 2 H z - f r e q u e n c y$$ $$v = \lambda * v = 3 2 \frac {m}{s}$$

Answer: $\lambda = 16m$ ; $v = 32\frac{m}{s}$

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