Final answer:
To find the velocity of the wave described by the equation y = 2\u00d710^-4 sin(100t - 50x), we compare it to the standard wave equation and use the relationship v = ω/k, where ω is the angular frequency and k is the wavenumber. The calculated velocity of the wave is 2 m/s.
Step-by-step explanation:
The equation of a plane progressive wave is given as y = 2\u00d710^-4 sin(100t - 50x). To find the velocity of the wave, we need to compare this equation with the standard wave equation y = A sin(kx - ωt), where A is amplitude, k is wavenumber, ω is angular frequency, and v is velocity. The wavenumber k and angular frequency ω are related to the velocity by the equation v = ω/k. In our wave equation, ω = 100 s^-1 and k = 50 m^-1. Therefore, the velocity of the wave v is calculated by dividing ω by k, leading to:
v = ω/k = 100 s^-1 / 50 m^-1 = 2 m/s.
Thus, the velocity of the wave is 2 m/s.