A sinusoidal wave in a rope is described by the wave function y=A sin( kx+ wt) A
ID: 2089243 • Letter: A
Question
A sinusoidal wave in a rope is described by the wave function y=A sin( kx+ wt) A=0.417 m, k= 0.954 m^-1, w= 30 rad/sec. x and y are in meters and t is in seconds
a) what is the length of the string? the rope has a linear mass density of 3.2 g/m . the acceleration of gravity is 9.8 m/s^2 answer in m.
b) what is the velocity of the wave? answer in m/s
c) If the tension in the rope is provided by an arrangement like the one illustrated, what is the value of the suspended mass? Answer in units of kg
Explanation / Answer
A standing wave consists of two waves traveling in opposite directions, Take a fixed point on one of these waves (constant phase) Let k x + w t = 0 (a point moving along the axis) x / t = v = w / k = [30/sec / (.954/m)] = 31.4 m/s for the speed v = [F / (m/l)]^1/2 for a string under tension F = v^2 * (m/l) Solve for F and use m = F / g to get the required mass