Answer: y(x, y) = 2.14cos(6.04x - 8.29t)
wave speed (v) =1.38m/s,
wavelength ( λ) =59.6m
Amplitude (A) =2.14m
Wave number (k) =6.04
Angular frequency (ω) = 8.29rad/s
Explanation:
The wavelength is simply defined as the distance between 2 successive crest or trough.
From the question it has been stated that the crest are 59.6m apart, thus (λ) =59.6m.
The wave travels a total vertical distance of 4.28m, this simply implies that along the vertical axis of the sine graph, the wave traveled from maximum displacement to the positive y axis (+A) through the center (o) and to the maximum displacement to the negative axis (-A).
Meaning total vertical distance =2A where A=Amplitude
This amplitude is 4.28/2 = 2.14m
Wave number (k) =2π/(λ)
Where π=180°
Thus, k=2*180/59.6
K=360/59.6
K=6.04
To get the angular frequency of the wave(ω), we use the formulae above
(ω)=kv
Where v is the wave speed
v=vertical distance/time taken
v= 4.28/3.09= 1.31m/s
Thus
(ω)=kv=6.04 * 1.31 =8.29rad/s.
Equation of wave is below
y(x,t)=Acos(kx−ωt)
By slotting in the parameters we have that
y(x, y) = 2.14cos(6.04x - 8.29t)
Above is the mathematical equation that describes the wave.
