Two waves are generated on a string of length $4.0 \mathrm{m}$ to produce a three-loop standing wave with an amplitude of $1.0 \mathrm{cm}$. The wave speed is $100 \mathrm{m} {\mathrm{s}}^{-1}$. Let the equation for one of the waves be of the form $\mathrm{y}(\mathrm{x},\mathrm{t})={\mathrm{y}}_{\mathrm{m}}\sin (\mathrm{kx}+\mathrm{\omega t}).$ In the equation for the other wave, what are
(a) $y_m$ (b) $k$ and $\omega$ $\left(\mathrm{d}\right)$ the sing in front of $\mathrm{\omega }$?

Two sinusoidal waves with the same amplitude of $6.00 \mathrm{mm}$ and the same wavelength travel together along a string that is stretched along an $x$-axis. Their resultant wave is shown twice in the figure shown below, as valley $A$ travels in the negative direction of the $x$-axis by distance $d=56.0 \mathrm{cm} \mathrm{in} 8.0 \mathrm{ms}$. The tick marks along the axis are separated by $10 \mathrm{cm}$, and height $H$ is $8.0 \mathrm{mm}$. Let the equation for one wave be of the form $y\left(x,t\right)=y_m\sin \left(kx\pm \omega t+\omega \varphi \right)$, where ${\varphi }_1=0$ and you must choose the correct sign in front of $\omega .$ For the equation for the other wave, what are (a) $y_m$ (b) $k$ (c) $\omega$, (d) ${\varphi }_2$ and (e) the sign in front of $\omega ?$