A wave equation which gives the displacement | vedclass

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(D) Comparing the given equation $y = 10^4 \sin(60t + 2x)$ with the standard wave equation $y = a \sin(\omega t + kx)$:$1$. Since the sign between $\o

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(D) Comparing the given equation $y = 10^4 \sin(60t + 2x)$ with the standard wave equation $y = a \sin(\omega t + kx)$:$1$. Since the sign between $\omega t$ and $kx$ is positive,the wave is travelling in the negative $X$-direction.$2$. The angular frequency is $\omega = 60 \, rad/s$. The frequency $f$ is given by $f = \frac{\omega}{2\pi} = \frac{60}{2\pi} = \frac{30}{\pi} \, Hz$.$3$. The wave number is $k = 2 \, m^{-1}$. The wavelength $\lambda$ is given by $k = \frac{2\pi}{\lambda} \implies \lambda = \frac{2\pi}{k} = \frac{2\pi}{2} = \pi \, m$.$4$. The wave velocity $v$ is given by $v = \frac{\omega}{k} = \frac{60}{2} = 30 \, m/s$.Since all the statements are correct,the correct option is $(d)$.

$A$ wave equation which gives the displacement along the $Y$ direction is given by the equation $y = 10^4 \sin(60t + 2x)$,where $x$ and $y$ are in metres and $t$ is time in seconds. This represents a wave:

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