Final answer:
The wavelength of the wave represented by the wave function y(x,t)=0.02sin(3.13x)cos(512t) is approximately 2.00 meters. This is computed by using the relationship between the wave number and the wavelength, where the wave number k provided in the wave function is 3.13 m^-1.
Step-by-step explanation:
The student is asking about the wavelength of a wave when a string is vibrating in its third harmonic. The wave function provided is y(x,t)=0.02sin(3.13x)cos(512t), which represents a standing wave. The general form of a sinusoidal wave on a string is y(x, t) = A sin(kx - ωt), where A is the amplitude, k is the wave number, and ω is the angular frequency. The wave number k is related to the wavelength λ by the formula k = 2π/λ. Therefore, we can determine the wavelength λ by rearranging the formula to λ = 2π/k.
From the given wave function y(x,t)=0.02sin(3.13x)cos(512t), we can see that the wave number k is 3.13 m-1. By applying the formula for wavelength, we get:
λ = 2π/3.13 m-1 ≈ 2.00 meters
Therefore, the wavelength of the wave is approximately 2.00 meters.