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(C) The given equation is $y = 0.02 \cos \left( \frac{\pi}{2} + 50\pi t \right) \cos (10x)$.Comparing this with the standard stationary wave equation

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The speed of the constituent waves is $4 \, m/s$

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(C) The given equation is $y = 0.02 \cos \left( \frac{\pi}{2} + 50\pi t ight) \cos (10x)$.Comparing this with the standard stationary wave equation $y = A \cos(\omega t + \phi) \cos(kx)$,we get $k = 10 \, 	ext{rad/m}$ and $\omega = 50\pi \, 	ext{rad/s}$.$1$. Wavelength $\lambda = \frac{2\pi}{k} = \frac{2\pi}{10} = 0.2 \, m$. (Statement $B$ is correct).$2$. Nodes occur where $\cos(10x) = 0$,i.e.,$10x = (2n+1)\frac{\pi}{2}$. For $n=0$,$x = \frac{\pi}{20} \approx 0.157 \, m$. The statement $D$ is approximately correct in context of standard wave problems.$3$. Antinodes occur where $|\cos(10x)| = 1$,i.e.,$10x = n\pi$. For $x = 0.3 \, m$,$10x = 3$,which is not a multiple of $\pi$. Thus,$x=0.3$ is not an antinode. However,checking the wave speed: $v = \frac{\omega}{k} = \frac{50\pi}{10} = 5\pi \approx 15.7 \, m/s$.$4$. The speed of constituent waves is $v = \frac{\omega}{k} = 5\pi \, m/s \approx 15.7 \, m/s$. The value $4 \, m/s$ given in option $C$ is incorrect.

The equation of a wave disturbance is given as: $y = 0.02 \cos \left( \frac{\pi}{2} + 50\pi t \right) \cos (10 x),$ where $x$ and $y$ are in meters and $t$ is in seconds. Choose the wrong statement:

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