Final answer:
To fully describe a sine or cosine wave, information about the amplitude, period, phase shift, and frequency is required. An equation incorporating these elements provides a complete mathematical representation of the wave.
Step-by-step explanation:
The student is inquiring about various properties of a wave represented by a trigonometric function, such as a sinusoidal wave. To fully describe a wave mathematically, information about the amplitude, period, phase shift, frequency, and vertical shift is needed. The amplitude (A) represents the maximum displacement from the equilibrium position. The period (T) is the time taken for one complete cycle of the wave, which can be found using T=2π/ω where ω is the angular frequency. The frequency (f) is the number of cycles per unit time and is given by f=1/T. The phase shift (φ) indicates how much the wave is shifted horizontally. An equation such as x(t) = A cos(ωt + φ) or y(x, t) = A sin(kx - ωt + φ) includes all these properties and is sufficient to describe the wave fully.
The phase shift is typically needed in addition to the amplitude and period to fully describe the wave's displacement over time. Therefore, knowing just the amplitude and period does not provide a complete description of the wave's characteristics. In the context of the options provided, the correct response based on the information needed to fully describe a wave would be (b) No, there is additional information needed for completeness.