A transverse wave propagating along x-axis is represented by y(x, t) = 8.0 sin (0.5 π x - 4 π t -π /4) where x is in metres and t is in seconds. The speed of the wave is (a) 8 m/s (b) 4 π m/s (c) 0.5 π m/s (d) π /4 m/s.

Answer: (a). k = 0.5π m⁻¹, ω = 4π rad/s v = (ω)/(k) = (4π)/(0.5π) = 8 m/s So the answer is (a) 8 m/s.

A transverse wave propagating along x-axis is represented by y(x, t)… | NEET 2006 (AIPMT)

Q97NEET 2006 · AIPMTEasy

Progressive Wave Equation

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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Answer: (a)

$k = 0.5\pi\text{ m}^{-1}$ , $\omega = 4\pi\text{ rad/s}$
$v = \dfrac{\omega}{k} = \dfrac{4\pi}{0.5\pi} = 8\text{ m/s}$
So the answer is (a) $8\text{ m/s}$ .

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