(D) The standard equation of a transverse harmonic wave is $y(x, t) = A \sin(\omega t + kx)$.Comparing this with the given equation $y(x, t) = 5 \sin(

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(D) The standard equation of a transverse harmonic wave is $y(x, t) = A \sin(\omega t + kx)$.Comparing this with the given equation $y(x, t) = 5 \sin(6t + 0.003x)$,we get:Angular frequency $\omega = 6\,rad/s$.Wave number $k = 0.003\,cm^{-1}$.To convert $k$ into $m^{-1}$,we multiply by $100$ because $1\,cm^{-1} = 100\,m^{-1}$.So,$k = 0.003 \times 100 = 0.3\,m^{-1}$.The wave velocity $v$ is given by the formula $v = \frac{\omega}{k}$.Substituting the values,$v = \frac{6}{0.3} = 20\,ms^{-1}$.

Class 11 Physics Waves and Sound Wave Equation and Characteristics of Waves

Medium

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

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$10$
B
$5$
C
$30$
D
$20$

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Wave Equation and Characteristics of Waves

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

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