1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wave on a string: time from y=2mm to -2mm. Amp. & Omega given. Best method?

  1. Aug 25, 2009 #1
    1. The problem statement, all variables and given/known data

    If y(x,t) = (6mm)sin(kx + (600rad/s)t + theta) describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = +2 mm and y = -2 mm?

    All known data are stated in above problem.



    2. Relevant equations I got the answer by plotting it on a unit circle, which I describe below. But what I want to know is if there is a method particular to the use of the wave function itself to get the same answer?



    3. The attempt at a solution

    Because sinusoidal wave motion is exactly analogous to rotation in a unit circle, a .006m amplitude corresponds to a .006m radius(r = .006m), which together with y=.002m can be taken as arcsin(y/r) to yield the radian measure from P(x,0) to P(x, .002) on the circle. This = .34 radians. Since the motion is from .002m to -.002m you take .34*2 = .68rad. Then to find the fraction of 600rad you take .68/600 = .00113 which also represents the fraction of s=1 second in 600rad/s. Therefore it takes .00113s or 1.1ms to get from .002m to -.002m .

    Is there a more appropriate method for doing this?
     
  2. jcsd
  3. Aug 25, 2009 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    Not really. The algebraic method will have you write

    2 = (6mm)sin(kx + (600rad/s)t1 + theta)

    solve for t1 in terms of the arcsine, do the same for t2 with

    -2 = (6mm)sin(kx + (600rad/s)t2 + theta) and find the difference as

    Δt = t2-t1=(Arcsin(-1/3)-Arcsin(1/3))/600.

    Both methods involve taking the difference between two arcsines.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Wave on a string: time from y=2mm to -2mm. Amp. & Omega given. Best method?
  1. V = r times omega (Replies: 4)

Loading...