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The wave equation is

$$y = A\sin (\omega t \pm kx \pm \phi_i)$$

What exactly is kx?

Why it is needed? Why can't we directly represent wave as we represent SHM -

$$y = A\sin (\omega t + \phi)$$

I even read that between the waves there is a phase difference of π -

$$y = A\sin (\omega t - kx)$$ and $$y = A\sin (kx - \omega t)$$

What is the difference between these two waves and how do they calculated the phase difference between these two waves?

Can someone please show me the derivation of the wave equation?

Now regarding frequency what I know is that freqeuncy is the number of oscillations or cycles per second.

If a wave is travelling in a string then does one cycle means motion of wave to and fro the string i.e. if the wave starts from one end reflects from other and again reaches first then could this be called as one cycle?

$$y = A\sin (\omega t \pm kx \pm \phi_i)$$

What exactly is kx?

Why it is needed? Why can't we directly represent wave as we represent SHM -

$$y = A\sin (\omega t + \phi)$$

I even read that between the waves there is a phase difference of π -

$$y = A\sin (\omega t - kx)$$ and $$y = A\sin (kx - \omega t)$$

What is the difference between these two waves and how do they calculated the phase difference between these two waves?

Can someone please show me the derivation of the wave equation?

Now regarding frequency what I know is that freqeuncy is the number of oscillations or cycles per second.

If a wave is travelling in a string then does one cycle means motion of wave to and fro the string i.e. if the wave starts from one end reflects from other and again reaches first then could this be called as one cycle?

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