A transverse harmonic wave on a string is given by where and are in cm and in second. The wave velocity is ______ . [2023]

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Solution

Q.
A transverse harmonic wave on a string is given by $y (x, t) = 5 \sin (6 t + 0.003 x)$ where $x$ and $y$ are in cm and $t$ in second. The wave velocity is ______ ${ms}^{- 1}$ . [2023]

Ans.
(20)

$y (x, t) = 5 \sin (6 t + 0.003 x)$

$k = {0.003 cm}^{- 1}, ω = 6 rad/s, v = \frac{ω}{k}$

$\Rightarrow \frac{6}{0.003 \times 10^{2}} = {20 ms}^{- 1}$

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