Question 212: Waves

Question

A wave travelling along the $$x$$-axis is described by the equation $$y(x, t)=0.005$$ $$\cos \,\left( {\alpha \,x - \beta t} \right).$$ If the wavelength and the time period of the wave are $$0.08$$ $$m$$ and $$2.0s$$, respectively, then $$\alpha $$ and $$\beta $$ in appropriate units are

Accepted Answer

$$y\left( {x,t} ight) = 0.005\,\cos \left( {\alpha x - \beta t} ight)$$ (Given)
Comparing it with the standard equation of wave
$$y\left( {x,t} ight) = a\cos \left( {kx - \omega t} ight)$$ we get
$$k = \alpha $$ $$\,\,\,\,\,$$ and $$\,\,\,\,\,$$ $$\omega  = \beta $$
$$	herefore$$ $${{2\pi } \over \gamma } = \alpha $$ $$\,\,\,\,\,$$ and $$\,\,\,\,\,$$ $${{2\pi } \over T} = \beta $$
$$	herefore$$ $$\alpha  = {{2\pi } \over {0.08}} = 25\pi $$ $$\,\,\,\,\,$$ and  $$\,\,\,\,\,$$ $$\beta  = {{2\pi } \over 2} = \pi $$

Answer

$$\alpha  = 25.00\pi ,\,\beta  = \pi $$

Answer

$$\alpha  = {{0.08} \over \pi },\,\beta  = {{2.0} \over \pi }$$

Answer

$$\alpha  = {{0.04} \over \pi },\,\beta  = {{1.0} \over \pi }$$

Answer

$$\alpha  = 12.50\pi ,\,\beta  = {\pi  \over {2.0}}$$

Waves

A wave travelling along the $x-axis is described by the equation y(x, t)=0.005 \cos \,\left( {\alpha \,x - \beta t} \right). If the wavelength and the time period of the wave are 0.08 m and 2.0s, respectively, then \alpha and \beta $ in appropriate units are

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