Final answer:
The correct interpretation of the simple harmonic wave equation shows that the amplitude is 4 cm, the frequency is 1/18 Hz, and the wave travels in the positive x-direction. The wavelength is actually 10 cm, not 5 cm as suggested, and the wave speed is 0.0556 m/s, not 20 m/hour.
Step-by-step explanation:
Analysis of the Given Wave Equation
The wave equation provided is y = 4sin[it(t/9 - x/5) + 1/6], where i probably represents the imaginary unit, which should not be there for a real wave function. Assuming this is a typo and it should be π instead, the corrected wave equation is y = 4sin[π(t/9 - x/5) + 1/6]. This equation can be written in the standard form for a traveling wave: y(x, t) = Asin(kx - ωt + φ). From the given equation, the amplitude (A) is 4 cm, and the wave travels in the positive x-direction since the argument of the sine function is (-ωt + kx). Using the coefficients of t and x, we can determine the wave speed (v) and wavelength (λ).
The angular frequency (ω) is π/9 s⁻¹, and the wave number (k) is π/5 cm⁻¹. The frequency (f) of the wave is ω/(2π) which is 1/18 Hz, and the wavelength is given by 2π/k, which equals 10 cm, not 5 cm as suggested in one of the options. The wave speed v = fλ is (1/18 Hz)(10 cm) = 5/9 cm/s or 0.0556 m/s, not 20 m/hour. The direction is positive since the (x) term in the argument of the sine function is negative, indicating it travels in the positive x-direction.
Thus, the correct statements about the wave based on the provided equation are: a) The frequency of the wave is 1/18 Hz, and b) The wave is going in the +ve x direction. The other options provided are incorrect: c) The wavelength of the wave is not 5 cm, it is 10 cm, and d) The velocity of the wave is not 20 m/hour; it is much less.