Explanation:
The given equation represents a wave of the form:
y = A sin (kx - ωt)
where A = 0.4, k = 1/4 and ω = 8.

Speed of the wave:
The speed of the wave can be calculated using the relation:
v = ω/k

Substituting the given values, we get:
v = 8/(1/4) = 32 m/s

Therefore, the speed of the wave is 32 m/s.

Explanation of the equation:
The equation y = 0.4 sin(8t-x/4) represents a wave with the following characteristics:

- Amplitude: The amplitude of the wave is 0.4 units.

- Wavelength: The wavelength of the wave can be calculated using the relation:
λ = 2π/k
where k is the wave number. Substituting the given value of k, we get:
λ = 2π/(1/4) = 8π

- Frequency: The frequency of the wave can be calculated using the relation:
f = ω/2π
where ω is the angular frequency. Substituting the given value of ω, we get:
f = 8/2π = 4/π

- Period: The period of the wave can be calculated using the relation:
T = 1/f
Substituting the value of f, we get:
T = π/4

- Phase velocity: The phase velocity of the wave can be calculated using the relation:
v_p = ω/k
Substituting the given values, we get:
v_p = 8/(1/4) = 32 m/s

- Group velocity: The group velocity of the wave can be calculated using the relation:
v_g = dω/dk
Substituting the given values, we get:
v_g = 0

Therefore, the wave does not exhibit any dispersion.