Wave Function - General Physics - Solved Past Paper, Exams of Physics

Download Wave Function - General Physics - Solved Past Paper and more Exams Physics in PDF only on Docsity! 8. (25 pts) A transverse wave on a string is described by the wave function y(x, t) = 0.12 sin(πx/8 + 4πt) where the amplitude is given in meters. a) (5 pts) What is the wavelength? By definition, k = 2π λ λ = 2π π/8 = 16 m b) (5 pts) How about the frequency? Again, by definition, ω = 2πf = 4π f = 2 Hz c) (5 pts) Determine the speed of the wave. v = fλ = (2)(16) = 32 m/s You could also use, from manipulation of the definitions, v = ω k = 4π π/8 = (4)(8) = 32 m/s It gives the same answer. Note that this is a wave on a string, not an EM wave. Thus the speed is not 3 × 108 m/s. d) (10 pts) Work out the speed of the actual string itself at t = 0.2 s for the piece of string at x = 1.6 m. The wave function describes the displacement of the medium (i.e. the string) from equilibrium. If we want how fast the string is moving (not the wave), then we need to find out how fast the displacement of the string is changing with time. Thus we need vstring = ∂y ∂t = 4π(0.12) cos(πx/8 + 4πt) Then just substitute the numbers (making sure your calculator is in radians!): v = 1.51 cos [ (1.6)(π) 8 + 4π(0.2) ] = −1.51 m/s I’m not too worried about the negative sign. That just means that at this point in space and time, the string is moving down.