Sebuah gelombang merambat menurut persamaan \(y = 18 \sin \pi (\frac 23 t - x + \frac 16)\) cm, dimana x dan t dalam meter dan detik. Titik P terletak pada jarak 5 meter dari sumber gelombang.
(A) kecepatan getaran titik P pada detik ke 10
\begin{equation*}
\begin{split}
y & = 18 \sin \left(\frac 23 t - x + \frac 16 \right) \\\\
v & = \frac {dy}{dt} \\\\
v & = 18 \:.\: \frac 23 \:.\: \cos \pi \left(\frac 23 t - x + \frac 16 \right) \\\\
v & = 12 \cos \pi \left(\frac 23 \:.\: 12 - 5 + \frac 16 \right) \\\\
v & = 12 \cos \left(3 \frac 16 \pi \right) \\\\
v & = 12 \cos \left(2 \pi + 1 \frac 16 \pi \right) \\\\
v & = 12 \cos \left(1 \frac 16 \pi \right) \\\\
v & = 12 \cos \left(\pi + \frac 16 \pi \right) \\\\
v & = 12 \:.\: - \cos \left( \frac 16 \pi \right) \\\\
v & = 12 \:.\: - \frac 12 \sqrt{3} \\\\
v & = -6 \sqrt{3} \text{ cm/s}
\end{split}
\end{equation*}
(B) percepatan getaran titik P pada detik ke 10
\begin{equation*}
\begin{split}
a & = \frac {dv}{dt} \\\\
a & = -12 \:.\: \frac 23 \:.\: \sin \pi \left(\frac 23 t - x + \frac 16 \right) \\\\
a & = -8 \sin \pi \left(\frac 23 t - x + \frac 16 \right) \\\\
a & = -8 \sin \pi \left(\frac 23 \:.\: 12 - 5 + \frac 16 \right) \\\\
a & = -8 \sin \left(3 \frac 16 \pi \right) \\\\
a & = -8 \sin \left(2\pi + 1 \frac 16 \pi \right) \\\\
a & = -8 \sin \left(1 \frac 16 \pi \right) \\\\
a & = -8 \sin \left(\pi + \frac 16 \pi \right) \\\\
a & = -8 \:.\: - \sin \left(\frac 16 \pi \right) \\\\
a & = -8 \:.\: - \frac 12 \\\\
a & = 4 \text{ cm/s}
\end{split}
\end{equation*}
