Final answer:
The standing wave equation for two cosine waves propagating in opposite directions with an amplitude of 5 volts, a frequency of 10 Hz, and a wavelength of 0.05 m, is y(x,t) = 10V cos(2π×10Hz×t) cos(2π×0.05m×x). This equation results from the superposition of the two individual cosine waves.
Step-by-step explanation:
To answer the student's question about two cosine waves of equal amplitude propagating in opposite directions and creating a standing wave, we would first need to write down the equation for the two waves and then combine them to form the standing wave equation. Given that the amplitude is 5 volts and the frequency is 10 Hz, the basic form of a wave moving in the positive x-direction could be represented as Acos(kx - ωt), where A is the amplitude, k is the wavenumber, and ω is the angular frequency. Similarly, the wave moving in the negative x-direction would be represented as Acos(kx + ωt). The standing wave results from the superposition of these two waves.
The wavenumber k can be found using the relation k = 2π/λ, and the angular frequency ω can be found using ω = 2πf. For the given wavelength λ = 0.05 m and frequency f = 10 Hz, we would use these to calculate k and ω before inserting them into the cosine functions.
The standing wave equation could then be written as:
y(x,t) = 2A cos(ωt) cos(kx)
Using the provided values, this would become:
y(x,t) = 10V cos(2π×10Hz×t) cos(2π×0.05m×x)
To plot the standing waves, one would typically use graphing software to input the equation and generate plots at the specified time values. Due to the format constraints here, we cannot provide these plots, but the instructions would involve setting up the axes, using the standing wave equation, and plotting for each time value t0 through t5.