How Do You Solve an Oscillating Rope Problem?

[tigers4]

Homework Statement

A rope, under tension of 120 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by
y = (1.18 m)sin ( x / 2) sin (10 t),
where x = 0 at one end of the rope, x is in meters, and t is in seconds.

(a) What is the length of the rope?

(b) What is the speed of the waves on the rope?

(c) What is the mass of the rope?

(d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation?

Homework Equations

v=sqrt(t/density)
d=m/v

The Attempt at a Solution

I have no clue how to start this problem, can anyone provide a way to approach a problem like this?

 

[vela]

What does the second harmonic look like? Specifically, how many nodes are there and where are they located on the string?

 

[tigers4]

the second harmonic has three nodes

 

[vela]

Right, there are nodes at the ends of the string and one right in the middle. Now try plotting y vs. x and seeing where its zeros are. Those zeros correspond to the nodes on the string.