Use the given formula to find the speed of the wave. Next, use the following relation between the speed v, the period T and the wavelength λ to find the period:
[tex]v=\frac{\lambda}{T}[/tex]a) Replace g=9.81 m/s^2 and d=0.75 cm (convert cm to m first) into the given formula:
[tex]0.75\operatorname{cm}=0.75\times10^{-2}m[/tex][tex]\begin{gathered} v=\sqrt[]{gd} \\ =\sqrt[]{(9.81\frac{m}{s^2})(0.75\times10^{-2}m)} \\ =0.27\frac{m}{s} \end{gathered}[/tex]b) Isolate T from the equation and substitute v=0.27 m/s, λ=2.6 cm.
[tex]2.6\operatorname{cm}=2.6\times10^{-2}m[/tex][tex]\begin{gathered} v=\frac{\lambda}{T} \\ \Rightarrow T=\frac{\lambda}{v} \\ =\frac{2.6\times10^{-2}m}{0.27\frac{m}{s}} \\ =0.096s \end{gathered}[/tex]Therefore, the speed of a wave in water that is 0.75 cm deep is 0.27 m/s, and if the wave has a wavelength of 2.6cm, its period is equal to 0.096s.
[tex]\begin{gathered} v=0.27\frac{m}{s} \\ T=0.096s \end{gathered}[/tex]
