(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Wave Speed questoin

**Physics Forums | Science Articles, Homework Help, Discussion**