transverse periodic wave is represented by the equation $\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)$. What is the direction of the velocity of the wave?
A) the $\mathrm{z}$ direction
B) the y direction
C) the $\mathrm{t}$ direction
D) the $\mathrm{x}$ direction

Question

Quizplus · Accepted Answer

The wave equation is given in terms of $z$ as a function of $y$ and $t$, indicating that the wave's displacement is in the $z$ direction, but the wave itself propagates along the $y$ direction. The presence of $y$ in the sine function's argument (indicating spatial variation) and $t$ for time variation shows that the wave moves along the $y$-axis.

Transverse Periodic Wave Is Represented by the Equation z(y,t)=1.50 cmsin⁡(1,250rad/st+10.0 m−1y)\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)z(y,t)=1.50 cmsin(1,250rad/st+10.0 m−1y)

Transverse Periodic Wave Is Represented by the Equation $\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)$