A progressive sinusoidal wave moving along the +x–axis is represented by .

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

A progressive sinusoidal wave moving along the +x–axis is represented by

y(x,t)=a\sin(kx-\omega t+\phi)

. (i) Prove that any two points that remain in the same phase at all instants satisfy the condition

kx-\omega t=\text{constant}

. (ii) Hence obtain an expression for the speed

v

of such a phase point in terms of

\omega

and

k

. (iii) Using the standard definitions of wavelength

\lambda

and frequency

\nu

, further show that

v=\lambda\nu