Question 512: Waves

Question

A transverse wave propagating along x-axis is represented by y(x, t) = 8.0 sin (0.5 $$\pi $$x $$-$$ 4$$\pi $$t $$-$$ $$\pi $$/4) where x is in metres and t is in seconds. The speed of the wave is

Accepted Answer

$$y\left( {x,t} ight) = 8.0\sin \left( {0.5\pi x - 4\pi t - {\pi  \over 4}} ight)$$
Compare with a standard wave equation,
$$y = a\sin \left( {{{2\pi x} \over \lambda } - {{2\pi t} \over T} + \phi } ight)$$
we get $${{2\pi } \over \lambda } = 0.5\pi  \Rightarrow \lambda  = {{2\pi } \over {0.5\pi }} = 4m$$
$${{2\pi } \over T} = 4\pi  \Rightarrow T = {{2\pi } \over {4\pi }} = {1 \over 2}\sec $$
$$\upsilon  = 1/T = 2\,Hz$$.
Wave velocity, $$v = \lambda \upsilon  = 4 	imes 2 = 8$$ m/sec.

Answer

8 m/s

Answer

4$$\pi $$ m/s

Answer

0.5$$\pi $$ m/s

Answer

$$\pi $$/4 m/s.

Waves

A transverse wave propagating along x-axis is represented by y(x, t) = 8.0 sin (0.5 $\pi x - 4\pi t - \pi $/4) where x is in metres and t is in seconds. The speed of the wave is

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