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Resultant Wave Equation

The displacem...

Question

The displacement $y$ of a particle in a medium can be expressed as $y = 10^{- 6} sin (110 t + 20 x + \frac{π}{4}) m$ , where $t$ is in second and $x$ in metre. The speed of the wave is

A

2000 m / s

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B

5 m / s

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C

20 m / s

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D

5 π m / s

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Solution

The correct option is B $5 m / s$
The equation can be written in the form of, $y = y_{0} sin (k t + λ x + ϕ)$

where, $k = 100 / s$ and $λ = 20 / m$

The velocity of a travelling wave is given by, $v = k / λ$

Hence, substituting the values, $v = 100 / 20 = 5 m / s$

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