How can the direction of propagation help in determining the phase of a wave?

AI Thread Summary
The discussion focuses on determining the phase φ of a sinusoidal wave using the wave equation y(x,t) = y_max sin(kx - ωt + φ). The parameters k and ω are derived from the wavelength and frequency, respectively. The challenge arises when solving for φ, as both 0 and π satisfy the condition y(0,0) = 0, leading to ambiguity without additional initial conditions. Participants note that the direction of propagation is crucial in resolving this ambiguity. Ultimately, the lack of sufficient information prevents a definitive conclusion about the phase.
Philip551
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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?
 
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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.
 
kuruman said:
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
 
Philip551 said:
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.
 
haruspex said:
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:

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