Question

2) [10 marks How does the speed of deep water waves depend upon their wavelength (you may neglect surface tension and the depth of the water)? How does the period of oscillation of a drop of water depend upon its radius (you may neglect gravity and any interaction of the drop with its surroundings)? Estimate the length-scale at which the transition from gravity to surface tension being the dominant process to consider occurs. [The surface tension of water is approximately 72 mNm-1.]

Answer 1

How does the speed as deep water wave depends upon their wavelength. For deep water, Too many layers occurs so the friction will be lower and per lower friction the speed as deep water is going to be higher and the wavelength lambda = v/f (where lambda rightarrow larger) = > v = f . lambda = > v proportional to lambda Therefore we can say that speed as deep water is directly proportional to their wavelength How does the period as oscillation as a drop as water depends upon its radius Let say, the period as oscillation, T = rho r y where rho rightarrow density r rightarrow radius y rightarrow surface tension we will take dimension, [s] = [m^- L^-3 T^0] [r] = [m^0 L^1 T^0], [y] = [m^- L^0 T^-3] Hence [T^1] = [m^- L^-3 T^0] [m^0 L^1 T^0] [m^1 L^0 T^-3]