Final answer:
The student is confused about differentiating displacement with respect to time to find the velocity of medium particles in a wave. The differentiation should indeed be with respect to time, and the provided equation should have a negative sign, which seems to be a typo in the book.
Step-by-step explanation:
The question involves the concept of differentiation in physics, specifically relating to wave motion. The confusion arises from the differentiation with respect to y instead of t (time) when finding the velocity of medium particles in a wave. The velocity of the medium is given by the partial derivative of the displacement s(x,t) with respect to time t, while treating position x as a constant. In the context of waves, particularly transverse waves, the particles of the medium oscillate in the y-direction as the wave moves in the x-direction; hence, we find how this displacement changes with time to get the medium particle velocity at a particular point in space.
To clarify the equation provided, v(x,t)=∂/∂y(s(x,t))=s_max ω sin(kx−ωt+ϕ), it seems there's a typo: the differentiation should be with respect to t, not y. The equation should have a negative sign if we're considering the wave equation s(x,t) = s_max cos(kx - ωt + ϕ), leading to v(x,t) = -s_max ω sin(kx - ωt + ϕ) after differentiation with respect to time, which correctly indicates the velocity of the medium's particles.