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Oscillations

Question

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A wave is represented by the equation y= 0.5 sin(10t $-$ x) metre It is a travelling wave propagating along +x direction with velocity

10 m s^-1

20 m s^-1

5 m s^-1

None of these

Solution

A.

10 m s^-1

Compare the given eqution y = 0.5 sin (10t $-$ x) with the standard form

y = r sin $[\frac{2 π t}{T} + \frac{2 π x}{λ}]$

$\frac{2 π}{T}$ = 10

$\frac{2 π}{λ}$ = 1

⇒ $v = \frac{λ}{t}$

= $\frac{10}{1}$

⇒ v = 10 m/s

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