A string is tied to a mass on a spring. The mass oscillates 5 times each second, getting as far as \(8.0 \mathrm{~cm}\) from equilibrium, generating a wave on the string whose crests are separated by \(7.2 \mathrm{~m}\text{.}\) Find the following:
You create three waves on three identical strings that have the same period \(T\text{,}\) but they start at a maximum displacement at different times: \(y_{\text{max}}\) occurs at \(t=0\) for wave 1, at \(t=T/6\) for wave 2, and at \(t=5T/6\) for wave 3.
You are watching a leaf bobbing up and down on the surface of a lake (both above and below the surface of the water). You measure the leaf’s highest point above the surface of the water to be \(12 \mathrm{~cm}\text{.}\) After \(3 \mathrm{~s}\text{,}\) the leaf returns to its highest point above the surface of the water.
How do you think you could use your equation for the position of the leaf to write an equation for the vertical displacement of the water a distance \(x\) away from the leaf? Try writing such an equation!
In the water tab, what do you think would happen if you placed a leaf on the surface of the water near the right edge of the tank? Draw a displacement vs. time graph (like those provided in the simulation) for the leaf.
