A wave on the surface of water is given by y(x,t)=asin(kx−ωt+ϕ).
(i) Starting from the above relation, derive an expression that connects the speed of the wave with its wavelength and frequency.
(ii) If ω=157rads−1, convert this angular frequency into ordinary frequency expressed in hertz.
(iii) Prove that the numerical value of the amplitude obtained from the wave equation is independent of the phase constant ϕ.