The correct option is D y(x,t)=(4 cm)cos[(1.68 rad/s)t−(0.42 cm−1)x]
Given that, amplitude (A)=4 cm and wavelength λ=15 cm
K=2πλ=2π15=0.42 cm−1
The wave travelled a distance 2.4 m in 0.6 sec. Hence speed of the wave
v=2.40.6=4 cm/s
∴ angular frequency (ω)=v×K
=4×0.42=1.68 rad/s.
Since the wave is travelling along positive x-direction and crest X was at x=0 at t=0, so we can write the wave equation as
y(x,t)=Acos(Kx−ωt)
or y(x,t)=Acos(ωt−Kx)
[as cos(−θ)=cosθ]
Therefore , the desired equation is
y(x,t)=(4 cm)cos[(1.68 rad/s)t−(0.42 cm−1)x]