Final answer:
The amplitudes of the two individual waves in the given rope oscillation equation are both 0.2 m, determined by the coefficients in front of the sine and cosine functions.
Step-by-step explanation:
The amplitude of the two individual waves that make up the superposed wave of the rope can be determined by looking at the wave function y=0.2 m·sin(π/10·x)·cos(32π·t). This equation is the product of two separate sine and cosine functions, which represent two waves that have been superimposed. The amplitudes of such sine and cosine functions can be found by considering the coefficients in front of them. For the sine function that varies with respect to space, the amplitude is the coefficient directly in front of the sine term. For the cosine function that varies with respect to time, the amplitude is the coefficient directly in front of the cosine term.
The amplitude of the spatial wave function sin(π/10·x) and the temporal wave function cos(32π·t) are both given by the same coefficient, which is 0.2 m. Therefore, the amplitudes of the individual waves without superposition are both 0.2 m.