How does wave direction determine phase constant from initial conditions?

[Philip551]

Homework Statement

Find the wavefunction of a sinusoidal wave that propagates on a string towards the negative direction of the x-axis given that $y_{max}$ = 8cm, f = 3Hz, $\lambda$ = 80cm and that y(0,t)=0 at t=0.

Relevant Equations

$$y(x,t)= y_{max} sin(kx- \omega t + \phi)$$

Using the equation above I know that I have to find parameters k $\omega$ and $\phi$.

$$k = \frac{2\pi}{\lambda}$$

and

$$\omega = 2\pi f$$

The problem I've been having is how you would go about finding $\phi$ since by solving:

$$y(0,0)=0 \rightarrow sin(\phi)=0 \rightarrow \phi = 0, \pi $$

you get two different possible values for phi. How would you decide which one is correct without another initial condition?

 

[kuruman]

Why is $y(0,0)=0$? Note that you should write $y(x,t)=y_{max}\sin(kx-\omega t+\phi)$ not $y(x,t)=y_{m}ax\sin(kx-\omega t+\phi)$. The amplitude in LaTeX should be (without the delimiters) y_{max} not y_max.

 

[Philip551]

Why is $y(0,0)=0$? Note that you should write $y(x,t)=y_{max}\sin(kx-\omega t+\phi)$ not $y(x,t)=y_{m}ax\sin(kx-\omega t+\phi)$. The amplitude in LaTeX should be (without the delimiters) y_{max} not y_max.

I understood that y(0,t)=0 at t =0 (from the homework statement)is the same as y(0,0)=0

 

[haruspex]

Homework Statement:: Find the wavefunction of a sinusoidal wave that propagates on a string towards the negative direction of the x-axis given that $y_{max}$ = 8cm, f = 3Hz, $\lambda$ = 80cm and that y(0,t)=0 at t=0.
Relevant Equations:: $$y(x,t)= y_{max} sin(kx- \omega t + \phi)$$

Using the equation above I know that I have to find parameters k $\omega$ and $\phi$.

$$k = \frac{2\pi}{\lambda}$$

and

$$\omega = 2\pi f$$

The problem I've been having is how you would go about finding $\phi$ since by solving:

$$y(0,0)=0 \rightarrow sin(\phi)=0 \rightarrow \phi = 0, \pi $$

you get two different possible values for phi. How would you decide which one is correct without another initial condition?

Yes, there is not enough information to determine the phase exactly.
But you seem to have ignored the info about the direction of propagation.

 

[Philip551]

Yes, there is not enough information to determine the phase exactly.
But you seem to have ignored the info about the direction of propagation.

That is what I though.

I forgot to include that. It should be:

$$y(x,t) = y_{max} sin(kx+\omega t + \phi)$$