Q.The amplitude of a wave is represented by $y=0.2\sin\left[2\pi\left(25t-\dfrac{x}{0.4}\right)\right]$ in SI units. Find

[!TLDR] Writing the wave as $y=0.2\sin\left[2\pi\left(25t-\frac{x}{0.4}\right)\right]$ in the standard form $y=A\sin[2\pi(nt-x/\lambda)]$ directly reads off amplitude, frequen …

The wave equation is given in the standard textbook form $y=A\sin\left[2\pi\left(nt-\dfrac{x}{\lambda}\right)\right]$, which directly matches the general progressive-wave equation of section 6.2 once $n=\omega/2\pi$ and $\lambda=2\pi/k$ are substituted. Comparing $y=0.2\sin\left[2\pi\left(25t-\dfrac{x}{0.4}\right)\right]$ term by term against this standard form: the coefficient multiplying the whole sine is the AMPLITUDE, $A=0.2$ m; the coefficient of t inside the bracket is the FREQUENCY, $n=25$ Hz; and the denominator of the x-term inside the bracket is …

Match the given wave equation to the standard form $y=A\sin[2\pi(nt-x/\lambda)]$ and read off A …

Confusing the wavelength (denominator of the x-term) with the wave number k (its reciprocal, times $2\pi$), or mis-reading the coefficient of t as the angular frequency $\omega$ instead of the o …