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Frequency

A progressive...

Question

A progressive wave equation is given as: $y = 0.5 sin (10 π t - 5 x)$ , where $x$ and $y$ are 𝑖𝑛 $c m$ and $t$ is in $second$ . The maximum velocity $(in c m / s)$ of the particle is $x π$ . Find $x$ .

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Solution

Given, equation of progressive wave
$y = 0.5 sin (10 π t - 5 x)$
Equation of wave is
$y = A sin (ω t - k x)$
Comparing both the equations we get, $ω = 10 π$ and $k = 5$
The maximum velocity of the particle
$V = A ω = 5 π c m / s$
Final answer: $(5)$

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