Wave Speed questoin

blindzero678

1. The problem statement, all variables and given/known data

A rope, under a tension of 200 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by

y = (0.10m)(sinPIx/2)sin12PIt

where x = 0 at one end of the rope, x is in meters, and t is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation?


2. Relevant equations

I'm not sure...I know how to solve for the lenght of the rope, but I don't know which formula to use to solve for the wave speed. Although once i find this, I know how to find the mass of the rope and the period in part (d).

3. The attempt at a solution

I know you can find the length of the rope by setting

0.10 = 0.10sin(PIx/2)

because the 0.10 m in the original equation will be the amplitude of the wave, and at it's maximum, sin(12PIt) = 1. this gives you x = 1 meter.

But i don't know where to go from here, to get the velocity.

i know f = v/lambda = (nv)/(2L) and that lambda = 2L/n, but you can't use these equations to solve for velocity, because the v cancels out.

Redbelly98

There is a problem with (a). The answer does not depend on the amplitude.

Have you drawn a picture of the rope for the second-harmonic pattern? Do that, and think about how wavelength and rope length are related.