Question

8) In shallow water of depth d the speed of waves is approximately v=√gd. Find (a) the speed and (b) the period of a wave with a wavelength of 2.6 cm in water that is 0.75 cm deep.

Answer 1

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:

`v=(\lambda)/(T)`

a) Replace g=9.81 m/s^2 and d=0.75 cm (convert cm to m first) into the given formula:

`\begin{gathered} v=\sqrt[]{gd} \\ =\sqrt[]{(9.81(m)/(s^2))(0.75*10^(-2)m)} \\ =0.27(m)/(s) \end{gathered}`

b) Isolate T from the equation and substitute v=0.27 m/s, λ=2.6 cm.

`\begin{gathered} v=(\lambda)/(T) \\ \Rightarrow T=(\lambda)/(v) \\ =(2.6*10^(-2)m)/(0.27(m)/(s)) \\ =0.096s \end{gathered}`

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.

`\begin{gathered} v=0.27(m)/(s) \\ T=0.096s \end{gathered}`