The equation of a wave is given as y = 0.07 s | vedclass

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Question

(A) The standard wave equation is $y = a \sin(kx - \omega t)$.Comparing the given equation $y = 0.07 \sin(12\pi x - 3000\pi t)$ with the standard form

Vedclass · Accepted Answer

$\lambda = 1/6 \ m, \ v = 250 \ m/s$

Vedclass · Answer

(A) The standard wave equation is $y = a \sin(kx - \omega t)$.Comparing the given equation $y = 0.07 \sin(12\pi x - 3000\pi t)$ with the standard form:Amplitude $a = 0.07 \ m$.Angular wave number $k = 12\pi \ rad/m$.Angular frequency $\omega = 3000\pi \ rad/s$.We know that $k = \frac{2\pi}{\lambda}$,so $\lambda = \frac{2\pi}{k} = \frac{2\pi}{12\pi} = \frac{1}{6} \ m$.We know that $\omega = 2\pi n$,so frequency $n = \frac{\omega}{2\pi} = \frac{3000\pi}{2\pi} = 1500 \ Hz$.The wave velocity $v = \frac{\omega}{k} = \frac{3000\pi}{12\pi} = 250 \ m/s$.Thus,the correct values are $\lambda = 1/6 \ m$ and $v = 250 \ m/s$.

The equation of a wave is given as $y = 0.07 \sin (12\pi x - 3000\pi t)$. Where $x$ is in $m$ and $t$ is in $s$,then the correct statement is:

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