Final answer:
The speed of the wave is 5.34 m/s.
Step-by-step explanation:
The wavefunction given is y(x,t) = 0.004 sin(44.5x + 237.0t).
To find the speed of the wave, we need to determine the wave speed. The wave speed is given by the formula v = λf, where λ is the wavelength and f is the frequency.
From the wavefunction, the wavelength can be found as λ = 2π/k, where k is the wave number. Comparing this with the given expression, we have k = 44.5m⁻¹.
The frequency can be found from the angular frequency using the formula f = ω/2π, where ω is the angular frequency. Comparing this with the given expression, we have ω = 237.0s⁻¹.
Substituting these values into the formula v = λf, we have v = (2π/k)(ω/2π) = ω/k = (237.0s⁻¹)/(44.5m⁻¹) = 5.34m/s.