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Phase and the General Equation

The equation ...

Question

The equation $y = 5 sin (3 x / 50) cos (450 t)$ represents the stationary wave setup in a vibrating sonometer wire, where $x, y$ are in $c m$ and $t$ in second. The velocity of one of the two progressive waves in that stationary wave is

2.7 m s - 1

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27 m s^{- 1}

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7.5 m s^{- 1}

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75 m s^{- 1}

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Solution

The correct option is C $75 m s^{- 1}$
$y = 5 sec (3 x / 50) cos (450 t)$
So, $k = \frac{3}{50}$ and $ω = 450$
$ν = \frac{ω}{k} = \frac{450}{^{3} /_{50}} c m / s$
$= \frac{450 \times 50}{3} c m / s$
$= \frac{450 \times 50}{3 \times 100} m / s$
$= 75 m / s .$

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