Question

the oscillations of two points x1 and x2 at x=0 and x=1m respectively are modelled as follows:y1=(0.3sin4 pie t) and y2=0.3sin(4 pie t+pie/8).calculate the wavelength and speed of the associated wave.

Answer 1

Answer on Question #66258 - Physics / Mechanics | Relativity

Question

The oscillations of two points x1 and x2 at x=0 and x=1m respectively are modelled as follows: y1=(0.3sin4 pie t) and y2=0.3sin(4 pie t+pie/8). calculate the wavelength and speed of the associated wave.

Solution

$$y1 = 0.3 \sin(4\pi t); y2 = 0.3 \sin\left(4\pi t + \frac{\pi}{8}\right)$$ $$\Delta \varphi = \frac{\pi}{8}; \Delta x = 1\,m;$$ $$\lambda = \frac{2\pi * \Delta x}{\Delta \varphi} = 2 * \frac{1}{\frac{1}{8}} = 16\,m - \text{wavelength}$$ $$\omega = 4\pi = 2\pi\nu; \quad \nu = 2\,Hz; \quad - \text{frequency}$$ $$v = \nu\lambda = 2 * 16 = 32\, \frac{m}{s}$$

Answer: wavelength: 16m, speed: 32 m/s

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