The speed (V) of wave on surface of water is given by
`V=sqrt((a lamda)/(2pi)+(2pib)/(rho lamda))`
where `lamda` is the wavelength of the wave and `rho` is density of water. a is a constant and b is a quantity that changes with liquid temperature.
(a) Find the dimensional formulae for a and b.
(b) Surface wave of wavelength 30 mm have a speed of `0.240 ms^(-1)`. If the temperature of water changes by `50^(@)C`, the speed of waves for same wavelength changes to `0.230 ms^(-1)`. Assuming that the density of water remains constant at `1 xx 10^(3) kg m^(-3)`, estimate the change in value of ‘b’ for temperature change of `50^(@)C`.

Answer

(a) `[a]=[M^(@)L^(1)T^(-2)];[b]=[M^(1)L^(@)T^(-2)]`
(b) `Delta b = -0.022 kg s^(-2)`