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Transverse Wave speed and acceleration

  • Thread starter ironlee
  • Start date
1. Homework Statement

A Transverse wave on a string is described by this function :

y=.25(meters) sin[[tex]\frac{\pi(4)}{8}[/tex] + [tex]\pi[/tex]4t]

a.) Find the speed of the wave at t= 2sec

b.) Find the acceleration at t= 2sec

2. Homework Equations

y=.25 sin[[tex]\frac{\pi(4)}{8}[/tex] + 4[tex]\pi[/tex]t]

3. The Attempt at a Solution

I tried taking the derivative with respect to t, but man I can't figure it out for the love of god and I have no idea what I'm doing wrong. I doubted myself so much I don't even know if I need to take the derivative.

P.S. at the end of the equation its 4 * pi * t (not 4 to the power of Pi) and its .25 meters
 
Are you sure you meant to write

[tex]0.25 \sin{\left(\frac{4\pi}{8}+4\pi t\right)}[/tex]

because there isn't any spatial coordinate in that wave function.

Either way, for a transverse wave, the argument of the function is constant, so

[tex]\frac{d}{dt}\left(kx-\omega t\right)=k\frac{dx}{dt}-\omega=\frac{d}{dt}C=0[/tex]

where [itex]k[/itex] is the wave number and [itex]\omega[/itex] is the angular frequency. Therefore the velocity is [tex]\frac{dx}{dt}=\frac{\omega}{k}[/tex]
 
Thank you so much! That'll be it, makes sense and yeah, that is what I meant to write. My problem was I couldn't remember which were constant. Thanks again!
 
Oh ok, great, I thought that's what you meant. Glad to help.
 

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