Consider a sinusoidal transverse progressive wave travelling along the +x–direction on a stretched string.
(i) Write the general mathematical expression for the displacement y(x,t) of such a wave in terms of its amplitude A, angular frequency ω, wave number k and initial phase ϕ.
(ii) Starting from the expression obtained in part (i), derive an expression for the speed v with which the wave profile propagates along the string and hence show that v=kω.
(iii) Using your result, further show that v=λf, where λ is the wavelength and f the frequency of the wave.