(a) Starting from the general equation of a progressive harmonic wave
y(x,t)=Asin(kx−ωt+ϕ),
show that the speed v of the wave is given by v=ω/k.
(b) A wave on a wire is described by
y(x,t)=0.02sin(5x+20t+6π)(SI units).
Identify:
(i) its amplitude,
(ii) its angular frequency,
(iii) its wavelength, and
(iv) its speed.
(c) For the wave in part (b), state with reasoning whether it travels in the +x or −x direction.
(d) Write an equation for another wave that has the same amplitude and speed as the wave in part (b) but propagates in the opposite direction while possessing zero initial phase at the origin (x=0,t=0).