I'm given the following problem:

For a harmonic travelling wave travelling in the positive direction, the initial transverse speed is 3 m/s and the initial $y$ displacement or transverse displacement is 0.1m. If the frequency of oscillation is 10 Hz, find amplitude and $\phi$ constant.

It's not a difficult problem. However, I do not understand initial speed and initial y displacement conditions.
Namely, I don't understand the following:

The general wave formula is:
y(x,t) = Asin(kx - wt + phi) and if initial "y" displacement is 0.10, then
y(0, 0) = 0.1 and then 0.1 = Asin(phi) and
u(0, 0) = 3 and 3 = -Acos(phi).

How do we know that x in these formulas will be zero?

And could someone explain me, why when we derive y(x,y) to get u(x,t), we must keep x as a constant ?


The wave equation likes three variables together.
$y$ the displacement of a particle from its equilibrium position, at a position $x$ front the origin/source, at a time $t$.

The word "initial" is used twice in the formulation of the problem and without any further information you can interpret that as $x=0$ and $t=0$.

So you have been given two piece of information about a particle at the origin $x=0$ at a time $t=0 which is undergoing simple harmonic motion so that you can find the two unknowns: the amplitude and the phase.

When you differentiate $y$ with respect to $t$ you are evaluating the velocity of a particle at a fixed position $x$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.