Transverse Wave speed and acceleration

[ironlee]

Homework Statement

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

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

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

b.) Find the acceleration at t= 2sec

Homework Equations

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

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

 

[jeffreydk]

Are you sure you meant to write

$$0.25 \sin{\left(\frac{4\pi}{8}+4\pi t\right)}$$

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

$$\frac{d}{dt}\left(kx-\omega t\right)=k\frac{dx}{dt}-\omega=\frac{d}{dt}C=0$$

where $k$ is the wave number and $\omega$ is the angular frequency. Therefore the velocity is $$\frac{dx}{dt}=\frac{\omega}{k}$$

 

[ironlee]

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!

 

[jeffreydk]

Oh ok, great, I thought that's what you meant. Glad to help.